Robert Liptser
Doctor of Sci., Professor
Publications, Books
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R.S. Liptser and A.N.
Shiryayev, Statistics of Random Processes. Nauka, Moscow, 1974.
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R.S. Liptser and A.N.
Shiryayev, Statistics of Random Processes I, General Theory.
Springer Verlag, New York, 1977.
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R.S. Liptser and A.N.
Shiryayev, Statistics of Random Processes II, Applications. Springer
Verlag, New York, 1978.
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R.S. Liptser and A.N.
Shiryayev, Statystyka processov stochastycznych. Warszawa, 1981.
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R.S. Liptser and A.
Shiryayev, Theory of Martingales. Nauka, Moscow, 1986.
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R.S. Liptser and A.
Shiryayev, Theory of Martingales. Kluwer, Dordrecht, 1989.
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R.S. Liptser, S. Anulova,
A. Veretennikov, N. Krylov, and A.N.Shiryayev, Stochastic Calculus
(Survey of Probability Theory). 45, Nauka, Moscow, 1989.
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Anulova, S. V.,
Veretennikov, A. Yu., Krylov, N. V., Liptser, R.Sh, Shiryaev, A. N.
Stochastic calculus Probability theory, III, 1-253, Encyclopaedia
Math. Sci., 45, Springer, Berlin, 1998.
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R.S.Liptser and
A.N.Shiryayev, On a Bayes problem of sequential search in diffusion
approximation, Theory Probab. Appl., X, No. 1, 1965, pp. 192-199.
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R.S.Liptser, On control of
Wiener process, Cybernetics. No. 6, 1965, pp. 81-84.
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R.S.Liptser, On maximizing
of the confidential probability, Cybernetics. No. 1, 1966, pp.
82-86.
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M.L.Dashevski and
R.S.Liptser, Simulation of stochastic differential equations
connected with the problem of "disorder" on an analogue computer,
Automation and Remote Control. XXVII, No. 4, 1966, pp. 142-150.
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A.N.Kabalevski and
R.S.Liptser, On design of random functions generator for simulation
of Markov diffusion process on analog computers, Automation and
Remote Control. XXVII, No. 6, 1966, pp. 171-177.
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R.S.Liptser and I.V.Tyme,
On solution of problems of continuous time dual control, Automation
and Remote Control. No. 9, 1966, pp. 40-47.
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R.S.Liptser, Comparison of
linear and nonlinear filtering of some Markov processes, Theory
Probab. Appl. XI, No. 3, 1966, pp. 528-533.
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M.L.Dashevski and
R.S.Liptser, Application of conditional semi-invariants in problems
of non-linear filtering of Markov processes, Automation and Remote
Control. No. 6, 1967, pp.63-74.
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M.L.Dashevski and
R.S.Liptser, Approximate technique for non-linear, non-stationary
dynamic systems of Markov's processes, Automation and Remote Control.
No. 8, 1967, pp.34-43.
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M.L.Dashevski and
R.S.Liptser, Integration of first order partial differential
equations on analog computers, Sbornik Cybernetics and Control.
1967.
19. R.S.Liptser, Filtering and prediction of components of Markov
diffusion processes, Theory Probab. Appl. XII, No. 4, 1967, pp.
764-765.
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R.S.Liptser and
A.N.Shiryayev, Extrapolation of multi-dimensional Markov processes
from incomplete data,Theory Probab. Appl. XIII, No. 1, 1968, pp.
17-38.
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R.S.Liptser and
A.N.Shiryayev, Filtering, smoothing and predicting of diffusion
Markov processes from incomplete data, Theory Probab. Appl. XIII, No.
3, 1968, pp. 369-370.
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R.S.Liptser and
A.N.Kabalevski, Generator of random function, The Problems of
Radiotechniques. No. 2, 1968.
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R.S.Liptser and
A.N.Shiryayev, Non-linear interpolation of components of diffusion
Markov processes, Theory Probab. Appl. XIII, No. 4, 1968, pp.
602-620.
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R.S.Liptser and
A.N.Shiryayev, Non-linear filtering of diffusion Markov processes,
Proc. Steklov Inst. Math. 104, 1968, 163-218.
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R.S.Liptser, On predicting
and filtering for certain Markov processes I, Cybernetics. No. 3,
1968, pp. 63-70.
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R.S.Liptser, On predicting
and filtering some Markov processes II, Cybernetics. No. 3, 1968,
63-70.
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R.S.Liptser, On predicting
and filtering some Markov processes I, Cybernetics. No. 6, 1968, pp.
70-76.
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R.S.Liptser and
A.N.Shiryayev, Smoothing and filtering of jump component of Markov
process, Izvestiya Academy of Science USSR, ser. Math. 33, No. 4,
1968, pp. 901-914.
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R.S.Liptser and
A.N.Shiryayev, A density of probability measures corresponding to
processes of diffusion type, Izvestiya Academy of Science USSR, ser.
Math. 33, Mo. 5, 1968, pp. 1120-1131.
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R.S.Liptser and
A.N.Shiryayev, Statistics of conditionally Gaussian random
sequences, Proceedings of the Sixth Berkeley Symposium on
Mathematical Statistics and Probability. 1970, pp. 389-422.
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R.S.Liptser and
A.N.Shiryayev, On absolutely continuous measures corresponding
diffusion type processes with respect to Wiener measure, em
Izvestiya Academy of Science USSR, ser. Math. 36, No. 4, 1972, pp.
848-888.
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E.L.Djukovskii and
R.S.Liptser, On recursion method of calculation normal solution of
linear algebraic equations Journal of Computer Mathematics and
Mathematical Physics. No. 4, 1972, 843-857.
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R.S.Liptser, Equations of
near-optimal Kalman filter with a singular matrix of noise
covariance in observations, Automation and Remote Control. No. 1,
1974, pp. 35-41.
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R.S.Liptser, Conditional
Gaussian random processes, Problems for Transmission of Information.
No. 2, 1974, pp. 75-94.
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R.S.Liptser, Optimal
coding and decoding for transmission of Gaussian Markov signal by
noiseless feedback channel, Problems for Transmission of Information.
No. 4, 1974, pp. 3-15.
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E.L.Djukovskii,
R.S.Liptser, Computation of pseudo-inverse matrices, Journal of
Computer Mathematics and Mathematical Physics. No. 2, 1975, pp.
489-492.
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R.S.Liptser, Gaussian
martingales and Kalman - Bucy filter, Theory Probab. Appl. XX, No.
2, 1975, pp. 292-308.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, Martingale methods in the theory of point
processes, Workshop of random process theory, Druskinenkai, II,
1974. Vilnius, 1975, pp. 269-354.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, Criteria of absolute continuity of measures
corresponding to multivariate point processes, Proceedings of third
Japan-USSR Symposium on Theory of Probability, Lecture Notes in Math.
550, Springer-Verlag, 1976, pp. 232-252.
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R.S.Liptser, On a
representation of local martingales, Theory Probab. Appl. No. 4,
1976, pp. 718-726.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, On the question of absolute continuity and
singularity of probability measures, Math. USSR Sbornik. 33, No. 3,
1977, pp. 203-221.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, "Predictable" criteria for absolute continuity
and singularity of probability measures (the continuous time case)
Soviet Math. Dokl. 18, No. 6, 1977, pp. 1515-1518
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A.A.Yershov, R.S.Liptser,
A robust Kalman filter in discrete time, Automation and Remote
Control. No. 3, 1978, pp. 60-69.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, On absolute continuity of probability measures
for Markov-Ito processes, Stochastic differential systems, Filtering
and Control, Proceedings of the IFIP-WG 7/1 Working conference
Vilnius, Aug. 28 - Sep.2, Lecture Notes in Control and Information
Science. 25, Springer-Verlag, No. 2, 1978, pp. 114-128.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, Absolute continuity and singularity of local
absolutely continuous probability distributions. I, Math. USSR
Sbornik. 35, No. 5, 1979, pp. 631-680.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, Absolute continuity and singularity of local
absolutely continuous probability distributions. II, Math. USSR
Sbornik. 36, No. 1, 1980,pp. 31-58.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, Some limit theorems for simple point processes (a
martingale approach), Stochastics., No. 3, 1980.
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Ju.M.Kabanov, R.S.Liptser,
and A.N.Shiryayev, On the representation of integer-valued random
measures and local martingales by means of random measures with
deterministic compensators Math. USSR Sbornik. 39, No. 2, 1980,pp.
267-280.
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R.S.Liptser, Strong law of
large numbers for local martingales, Stochastics. No.3 , 1980.
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N.A.Kuznetsov, R.S.Liptser,
and A.P.Serebrobskiy, Optimal control and information processing in
continuous time (a linear system and quadratic functional)
Automation and Remote Control. No. 10 , 1980 ,pp. 47-53.
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R.S.Liptser and
A.N.Shiryayev, A functional limit theorem for semimartingales,
Theory Probab. Appl. 25, No. 4 , 1980, pp. 684-702.
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R.S. Liptser and A.
Shiryayev, Necessary and sufficient conditions in the functional
central limit theorem, Theory Probab. Appl. No.1, 1981, pp. 132-137.
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R.S. Liptser and A.N.
Shiryayev, On weak convergence of semimartingales to stochastic
processes with independent and conditional independent increments,
Mathem. Sb. 116 (158), 1981, pp. 299-323.
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Butov, A. A., Kuznetsov,
N. A., R. Sh. Liptser, B. M. Miler, E. Ya. Rubinovich, A. Ya.
Serebrovski, A.I. Yashin, Generalized observations control in
problems of stochastical optimization. Control science and
technology for the progress of society, Vol. 2 (Kyoto, 1981),
851-856, IFAC Proc. Ser. IFAC, Laxenburg, 1982.
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R.S. Liptser and A.N.
Shiryayev, Rate of convergence in the central limit theorem for
semimartingales. Theory. Probab. Appl., No.1, 1982, pp. 3-14.
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R.S.Liptser and
A.N.Shiryayev, The problem of "predictable" criteria of contiguity,
Fourth USSR-Japan Symposium Proceedings, 1982, Probability Theory
and Mathematical Statistics. Lecture Notes in Math. 1021, Springer-Verlag,
pp. 386-418.
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R.S. Liptser and A.N.
Shiryayev, On the problem of necessary and sufficient conditions in
the functional central limit theorem for local martingales,
Wahr.-theorie, verw. Geb. 59, 1982, pp. 311-318.
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R.S. Liptser, A.N.
Shiryayev, and F. Pukelsheim, Necessary and sufficient conditions
for contiguity and entire asymptotic separation of probability
measures, Russian Mathematical Surveys, London Mathematical Society.
37, No. 6, 1982, pp. 107-136.
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Yu.M.Kabanov, R.S. Liptser,
and A.N. Shiryayev, Strong and weak convergence of distributions of
counting processes, Theor. Probab. Appl. No. 2, 1983, pp. 288-319.
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R.S. Liptser and A.
Shiryayev, Invariance principle for semimartingales in "nonclassical"
formulation, Theory Probab. Appl. No. 1, 1983, pp. 3-31.
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R.S. Liptser and A.
Shiryayev, Weak convergence of semimartingales to diffusions Math.
USSR Sbornik 49 No. 1, 1984, pp. 171-195.
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R.S. Liptser and Yu.
Kabanov, On convergence in variation of the distributions of
multivariate point processes Wahr.-theorie verw. Geb. 63, 1983, pp.
475-485.
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R.S. Liptser, Yu. Kabanov,
and A. Shiryayev, Estimates of proximity in variation of probability
measures, Soviet. Math. Dokl. 30 No. 2, 1984, pp. 351-354.
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R.S. Liptser, E.
Krichagina, and E. Rubinovich, Kalman filter for Markov processes,
in book: Statistics and Control of Stochastic Processes, New York.
1984, pp. 197-213.
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Kabanov, Yu. M., Liptser,
R. Sh., Shiryaev, A. N. Estimates of closeness in variation of
probability measures. Akad. Nauk SSSR. 1984, no. 2, 265-268.
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R.S. Liptser, On a
functional limit theorem for Markov processes, in book: Statistics
and Control of Stochastic Processes, New York. 1984, pp. 305-316.
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R.S. Liptser and A.
Shiryayev, On contiguity of probability measures corresponding to
semimartingales Analysis Mathematica. No. 11, 1985, pp. 93-124.
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R.S. Liptser, A. Shiryayev,
and Yu. Kabanov, On the variation distance for probability measures
defined on a filtered space Theory Probab. Related Fields. 71, 1986,
pp. 19-35.
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R.S. Liptser, Ya. Kogan,
and A.Smorodinskii, Gaussian diffusion approximation of a closed
Markov model of a computer network Problems of Information
Transmission. 22, No.1, 1986, pp. 49-65.
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R.S. Liptser, E.
Krichagina, and A. Pukhalskii, Diffusion approximation for systems
with arrival depending on queue and arbitrary service, Theory Probab.
Appl. No.1, 1988, pp. 124-135.
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R.S. Liptser and A. Yashin,
Application of martingale methods, Automation and Remote Control.
No. 3, 1988, pp. 169-176.
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R.S. Liptser and J.
Stoyanov, Second order approximation for diffusion type processes,
Comptes rendus de l'Academie Bulgare des Science. No. 8, 1989, pp.
19-21.
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R.S. Liptser an A. Butov,
Diffusion approximation with reflection for a queueing model with an
autonomous server, in book: Stochastic Processes and Control of
Random Processes. Moscow, 1989.
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R.Liptser and J.Stoyanov,
Stochastic version of the averaging principle for diffusion type
processes, Stochastics and Stochastic Reports. 32, 1990, pp.
145-163.
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R.S. Liptser and
A.N.Shiryayev, Large deviation for martingales with independent and
homogeneous increments, in book: Probab. Theory and Mathematical
Statistics, Proceedings of the Fifth Vilnius Conf., July 25, 1989.,
1990, pp. 124-133.
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R.S. Liptser and S.
Anulova, Diffusion approximation for processes with normal
reflection. Theory Probab. Appl. No. 3, 1990, pp. 417-430.
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R.S. Liptser, Ergodic
theorem for the semimartingale-helix, in book: Festeschrift
Yu.Prohorov et al. VSP/Mokslas, 1991.
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R.S. Liptser and
W.Runggaldier, On diffusion approximation for filtering, Stochastic
Processes and their Applications. 38, 1991, pp. 183-189.
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P.Kind, R.S. Liptser, and
W. Runggaldier, Diffusion approximation in past dependent models and
applications to option pricing, The Annals of Applied Probability.
1, No. 3, 1991, pp. 379-405.
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R.S. Liptser, G.B. Di Masi,
and P.Kitsul, Minimal dimension linear filters for stationary Markov
processes with finite state space, Stochastics and Stochastics
Reports. 36, 1991, pp. 4-19.
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R.S.Liptser and
S.V.Lototsky, Diffusion approximation and robust Kalman filter,
Journal of Mathematical Systems, Estimation , and Control. 2, No. 3,
1992, pp. 263-274.
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R.S.Liptser,
A.A.Pukhalskii, Limit theorems on large deviations for
semimartingales, Stochastics and Stochastic Reports. 38, 1992, pp.
201-249.
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R.S.Liptser, Large
deviations for simple closed queueing model, Queueing Systems. 14,
1993, pp. 1-31.
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Ya. Kogan and R.S.Liptser,
Limit non-stationary behavior of large closed queueing network with
bottleneck, Queueing Systems. 14, 1993, pp. 33-55.
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R.S.Liptser, The Bogolubov
averaging principle for semimartingales, Proceedings of the Steclov
Institute of Mathematics. Moscow, No. 4, 1994.
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O.V. Gulinskii, R.S.
Liptser, and S.V. Lototskii, Large deviations for unbounded additive
functionals of Markov processes with discrete time, J. of Applied
Mathematics and Stochastic analysis, Florida. VII, No. 3, 1994.
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Y. Kogan, R.S. Liptser,
and M. Shenfield, State-dependent Bene·s buffer model with fast
loading and output rates, The Annals of Applied Probability. 5, No.
1, 1995, pp. 97-120.
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R.S. Liptser, W.J.
Runggaldier, Non-linear filters for linear models (A robust
approach), IEEE Transaction on Information Theory. 41, No. 4, 1995,
pp. 1001-1009.
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R. Liptser, Large
deviations for non-diffusion process. Statistics and control of
stochastic processes. Moscow, 1995/1996.
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R.S. Liptser, Large
deviations for occupation measure of Markov processes (discrete time
non compact case), Theory of Probab. Appl. Moscow, 41, No. 1, 1996,
pp. 65-88.
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R.S. Liptser, W.J.
Runggaldier, and M.Taksar, Deterministic approximation for
stochastic control problem, SIAM J. on Optimization and Control. 34,
No. 1, 1996, pp. 161-178.
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R. Liptser, Large
devataions for two scaled diffusions, Theory of Probability and
Related Fields. 106, 1996, pp. 71-104.
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F.C. Klebaner and R.
Liptser, Large deviations for for recurrent sequences with
aftereffect, Problems of Information Transmission. 32, 1996, No. 4,
pp. 23-34.
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Liptser R.Sh., Steinberg
Y., Bobrovski B.Z., and Schuss Z., Fixed lag smoothing of scalar
diffusions-Part I: the filtering-smoothig equation, Stochastic
Processes and their Application. 64, 1996, pp. 237-255.
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P.-L. Chow and R.
Khasminskii, and R.Sh. Liptser, Tracking of signal and its
derivatives in Gaussian white noise, Stochastic processes and their
application. 69, 1997, 2, pp. 259-273.
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M.L. Kleptsina, and A.P.
Serebrovski, and R.Sh. Liptser, Nonlinear Filtering problem with
contamination, The Annals of Applied Probability. 7, 1997, 4, pp.
917-934.
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R.S. Liptser, O. Zeitouni,
Robust diffusion approximation for nonlinear filtering, Journal of
Mathematical Systems, Estimation and Control. 8, 1, 1998, pp.
138-142. ttp://www.birkhauser.com/journals/jmsec/download.html
code 93647
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Liptser, R. and Muzhikanov,
P. Filtering with a Limiter (improved performance), Journal of
Applied Mathematics and Stochastic Analysis. 11, 3, 1998, pp.
289-300.
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Liptser, R. and Spokoiny,
V. Moderate Deviations for integral functionals of diffusion
process, Preprint. Weierstrass Institute, Berlin, 1998.
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O.V. Gulinskii, R.S.
Liptser, Example of large deviations for stationary process, Theory
of Probability and Applications. 44, 1, 1999, pp. 211-225.
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F. C. Klebaner and R.
Liptser, Moderate Deviations for Randomly Perturbed Dynamical
Systems, Stochastic Processes and their Applications. 80, 1999, pp.
157-176.
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R.S. Liptser and V.
Spokoiny, Moderate deviations type evaluation for integral
functionals of diffusion processes, EJP. 4, 1999, Paper 17. (http://www.math.washington.edu/
ejpecp/)
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Liptser and V. Spokoiny,
Deviation probability bound for martingales with applications to
statistical estimation. Stat. and Probab. Letters, 46, 2000, pp.
347-357.
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R.Sh.Liptser,
W.J.Runggaldier, and M.Taksar, Asymptotic Optimality for Stochastic
Control Problems via Diffusion Approximation, Theory of Probability
and Applications, 44, 4, 1999, pp.705-737.
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R.S. Liptser and A.N.
Shiryaev, Statistics of Random Processes I, General Theory (Second
edition). Springer, 2000.
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R.S. Liptser and A.N.
Shiryaev, Statistics of Random Processes II, Applications (Second
edition). Springer, 2000.
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R. Liptser, Moderate
deviation for dynamic model governed by stationary process, in book:
Skorokhod's ideas in Probability Theory, National Academy of Science
of Ukraine Institute of Mathematics, pp. 256-270, Kyiv, 2000.
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R. Liptser and V. Spokoiny,
On estimating a dynamic function of a stochastic system with
averaging. Statistical Inference for Stochastic Processes. 3:, pp.
225-349, 2000.
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Chigansky P., Liptser, R.
and Bobrovsky, B.Z. Simple asymptotically optimal filter over
infinite horizon. Journal of Applied Mathematics and Stochastic
Analysis. Vol. 14, 1, pp. 93-112, 2001.
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P.-L. Chow, R. Khasminskii,
R. Liptser On estimation of time dependent spatial signal in
Gaussian white noise, Stochastic Processes their Applications, 96
(2001), pp. 161-175 .
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R.S. Liptser and A.N.
Shiryayev, Statistics of Random Processes. I, General Theory.
(Second edition), Springer, Berlin (etc.) 2000.
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R.S. Liptser and A.N.
Shiryayev, Statistics of Random Processes. II, Applicationa. (Second
edition), Springer. Berlin etc, 2000.
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F. Klebaner and R. Liptser
Asymptotic Analysis and Extinction in a Stochastic Lotka-Volterra
model. Annals of Applied Probability. 11 (2001), 4 pp. 1263-1291.
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F. Carravetta, A. Germani,
R. Liptser, C. Manes. Filtering of nonlinear stochastic feedback
systems. SIAM J. Control Optim. 40 (2002), no. 5, pp. 1576-1584.
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N. Krylov, R. Liptser,
Diffusion approximation with discontinuous coefficients. Stochastic
Processes and their Applications. 102 (2002), 2, pp. 235-264.
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P. I. Kitsul, R. S.
Liptser and A. P. Serebrovski, Markovianity of a subset of
components of a Markov process, Systems & Control Letters. 46
(2002), 4, pp. 237-242.
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R. Khasminskii and R.
Liptser, On-line estimation of a smooth regression function. Theory
of Probability and its Applications. 3 (2002)
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Liptser, R., Spokoiny, V.
and Veretennikov, A.Yu., Freidlin-Wentzell type large deviations for
smooth processes. Markov Process and Relat. Fields. 8 (2002), pp.
611-636.
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R. Z. Khaminskii, F. C.
Klebaner, R. Liptser, Some results on the Lotka-Volterra model and
its small random perturbations. Proceedings of the Eighth Vilnius
Conference on Probability Theory and Mathematical Statistics, Part I
(2002). Acta Appl. Math. 78 (2003), no. 1-3.
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V. Abramov, R. Liptser, On
Existence of limiting distribution for time-nonhomogeneous countable
Markov process. Queueing Systems 46 (2004), pp. 353 361.
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P. Baxendale, P. Chigansky,
R. Liptser, Asymptotic stability of the Wonham filter: ergodic and
nonergodic signals. SIAM Journal on Control and Optimization. 43
(2004), no 2, pp. 643-659.
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P. Chigansky, R. Liptser,
Stability of nonlinear filters in non-mixing case, Annals of Applied
Probability 14, (2004), no 4, pp. 2038-2056
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B. Delyon, A.natoly
Juditsky and R. Liptser, Moderate Deviation Principle for Ergodic
Markov Chain. Lipschitz Summands. Shiryaev's Festschrift. (2005).
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R. Liptser and A. Novikov,
Tail Distributions of Supremum and Quadratic Variation of Local
Martingales. Shiryaev's Festschrift. (2005).
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A. Guillin, R. Liptser,
MDP for integral functionals of fast and slow processes with
averaging, Stochastic Processes, Applications, (2005) 115, 7,
1187-1207.
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L. Goldentayer, F.
Klebaner, and R. Sh. Liptser. , Tracking Volatility, Problems of
Information Transmission, 41, No. 3, 2005, 212-229. (Translated from
PROBLEMY PEREDAQI INFORMACII, No. 3, 2005, 32-50.
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A. Guillin and R. Liptser,
Examples of moderate deviation principle for diffusion processes.
Discrete and Continuous Dynamical Systems, Series B. Vol. 6, n. 4,
2006, 803-828.
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P. Chigansky and R.
Liptser, On role of predictor in the filtering stability. Elect.
Comm. in Probab. 11 (2006) 129-140.
Papers
Accepted for Publication
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L.Goldentayer and R.
Liptser, On-line tracking of a smooth regression function.
Statistical Inference for Stochastic Processes.
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F. Klebaner and R. Liptser.
Likely path to extinction in simple branching models with large
initial population. JAMSA
Papers
Submitted for Publication
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F. Klebaner and R. Liptser.
Ruin Analysis in Constant Elasticity of Variance Model with large
initial funds. Journal of Applied Probability.
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