Large deviations for stochastic systems with memory

Discrete and Continuous Dynamical Systems - Series B

Volumn 6, Issue 4, 2006, Pages 881-893

  Mohammed, Salah Eldin A ^a   Zhang, Tusheng ^b  

^a Southern Illinois University at Carbondale   (United States)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Large deviations; Stochastic systems with memory

Indexed keywords

EID: 33745319088     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. A. Dembo, and A. Zeitouni, Large Deviations Techniques and Applications, Springer-Verlag, Berlin Heidelberg, 1998.
2. F. den Hollander, Large deviations, Fields Institute Monographs, 14. American Mathematical Society, Providence, RI, (2000), pp.143
3. J.-D. Deuschel and D. W. Stroock, Large Deviations, Academic Press, Boston, San Diego, New York, (1989).
4. M. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, I, Comm. Pure Appl. Math., 28 (1975), 1-47.
5. M. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, II, Comm. Pure Appl. Math., 28 (1975), 279-301.
6. M. Donsker and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, III, Comm. Pure Appl. Math., 29 (1976), 389-461.
7. I. Elsanosi, B. Øksendal and A. Sulem, Some solvable stochastic control problems with delay, Stochastics Stochastics Rep., 71 (2000), no. 1-2, 69-89.
8. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984.
9. K. Itô and M. Nisio, On stationary solutions of a stochastic differential equation, J. Math. Kyoto University, 4-1 (1964), 1-75.
10. Kolmanovskii, V., and Myshkis, A., Introduction to the theory and applications of functional-differential equations, Mathematics and its Applications, 463, Kluwer Academic Publishers, Dordrecht (1999).
11. H. J. Kushner, On the stability of processes defined by stochastic differential-difference equations, J. Differential Equations, 4 (1968), 424-443.
12. X. Mao, Stochastic differential equations and their applications, Horwood Series in Mathematics &: Applications, Horwood Publishing Limited, Chichester, (1997), pp. 366.
13. V. J. Mizel, V. J. and VṪrutzer, Stochastic hereditary equations: existence and asymptotic stability, Journal of Integral Equations, 7 (1984), 1-72.
14. S.-E. A. Mohammed, Stochastic Functional Differential Equations, Research Notes in Mathematics, 99, Pitman Advanced Publishing Program, Boston, London, Melbourne (1984).
15. S.-E. A. Mohammed, Stochastic differential systems with memory: Theory, examples and applications, Stochastic Analysis and Related Topics VI, The Geilo Workshop, 1996, eds. L. Decreusefond, J. Gjerde, B. Øksendal and A.S. Ustunel, Progress in Probability, 42 (1998), Birkhauser.
16. M. Scheutzow, Qualitative behaviour of stochastic delay equations with a bounded memory, Stochastics, 12 (1984), no. 1, 41-80.
17. M. Scheutzow, Stationary and Periodic Stochastic Differential Systems: A study of qualitative changes with respect to the noise level and asymptotics, Habilitationsschrift, Fachbereich Mathematik, University of Kaiserslautern, Germany, 1988.
18. D.W. Stroock, An Introduction to the Theory of Large Deviations, Springer-Verlag, Berlin, 1984.
19. T.S. Zhang, On the small time asymptotics of diffusions on Hubert spaces, Annals of Probability, 28:2 (2000), 537-557.
20. T.S. Zhang, A large deviation principle of diffusions on configuration spaces, Stochastic Processes and Applications, 91 (2001), 239-254.