This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R. Azencott, "Grandes deviations et applications", Lecture Notes in Math., No. 774, 1980, Springer-Verlag, New York.
R. Azencott, G. Ruget, "Melanges d'equations differentialles et grands écartes à la loi des grand nombres", A. Wahr. 38, 1977, pp. 1–54.
A. D. Ventsel, M. I. Freidlin, "Some problems concerning stability under small random perturbations", Theory of Prob. and Applic., 17, 1972, pp. 269–283.
A. D. Ventsel, "Rough limit theorems on large deviations for Markov processes", I, II, Theory of Prob. and Applic., 21, 1976, pp. 227–242.
M. I. Freidlin, "The averaging principle and theorems on large deviations", Russian Math. Surveys, 33, July–Dec., 1978, pp. 117–176.
M. Donsker, S. R. S. Varadhan, "Asynptotic evaluation of certain Markov process expectations for large time", I, II, III, Comm. Pure Appl. Math. 28, 1975, pp. 1–47, 229–301, 389–461.
S. Karlin, "Positive operators", J. Math. and Mech., 8, 1959, pp. 907–937.
T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin, 1976.
N. Dunford, J. T. Schwartz, Linear Operations, Part I, Wiley, New York, 1966.
A. J. Viterbi, Principles of Coherent Communication, McGraw-Hill, New York, 1966.
F. L. Gardner, Phaselock Techniques, 2nd ed., 1979, Wiley, New York.
Z. Schuss, Theory and Applications of Stochastic Differential Equations, 1980, Wiley, New York.
D. Ludwig, "Persistence of dynamical systems under random perturbations", SIAM Rev. 17, 1975, pp. 605–640.
G. Ruget, "Some tools for the study of channel-sharing algorithms", CISM publication, ed. Longo, Springer, 1980.
H. J. Kushner, "A cautionary note on the use of singular perturbation methods for 'small noise’ models", Stochastics, 6, 1982, pp. 117–120.
B. Z. Bobrovsky, A. Schuss, "A singular perturbation method for the computation of the mean first passage time in a non-linear filter", SIAM J. on Appl. Math., 42, 1982, p. 174–187.
H. J. Kushner, "Robustness and approximations of escape times and large deviations estimates for systems with small noise effects", LCDS Report 1982, Lefschetz Center for Dynmaical Systems, Brown University.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Kushner, H.J. (1982). Approximation of large deviations estimates and escape times and applications to systems with small noise effects. In: Kohlmann, M., Christopeit, N. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 43. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044291
Download citation
DOI: https://doi.org/10.1007/BFb0044291
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12061-2
Online ISBN: 978-3-540-39518-8
eBook Packages: Springer Book Archive