On the stability of diffusion processes with state-dependent switching

Science in China, Series A: Mathematics

Volumn 49, Issue 9, 2006, Pages 1258-1274

  Xi, Fubao ^a   Zhao, Liqin ^b  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Coupling; Exponential ergodicity; Feller continuity; State dependent switching; Strong Feller continuity

Indexed keywords

EID: 33750220196     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-006-2017-1     Document Type: Article

References (27)

1. Xi F B. Stability of a random diffusion with nonlinear drift. Stat Probab Letters, 2004, 68: 273-286
2. Khas'minskii R Z. Stochastic Stability of Differential Equations. Alphen: Stijhoff and Noordhoff, 1980
3. Meyn S P, Tweedie R L. Stability of Markovian processes III: Foster-Lyapunov criteria for continuous-time processes. Adv Appl Probab, 1993, 25: 518-548
4. Skorohod A V. Asymptotic Methods in the Theory of Stochastic Differential Equations. Providence: Amer Math Soc, 1989
5. Basak G K, Bisi A, Ghosh M K. Stability of a random diffusion with linear drift. J Math Anal Appl, 1996, 202: 604-622
6. Basak G K, Bisi A, Ghosh M K. Stability of a degenerate diffusions with state-dependent switcing. J Math Anal Appl, 1999, 240: 219-248
7. Yuan C G, Mao X R. Asymptotic stability in distribution of stochastic differential equations with Markovian switching. Stoch Proc Appl, 2003, 103: 277-291
8. Xi F B. Stability for a random evolution equation with Gaussian perturbation. J Math Anal Appl, 2002, 272: 458-472
9. Chen M F. From Markov Chains to Non-Equilibrium Particle Systems. Singapore: World Scientific, 1992
10. Chen M F, Li S F. Coupling methods for multidimensional diffusion processes. Ann Probab, 1989, 17: 151-177
11. Freidlin M I, Wentzell A D. Random Perturbations of Dynamical Systems. New York: Springer-Verlag, 1984
12. Xi F B. Invariant measure for the Markov process corresponding to a PDE system. Acta Math Sinica, English Ser, 2005, 21: 457-464
13. Dawson D A, Zheng X G. Law of large numbers and central limit theorem for unbounded jump mean-field models. Adv Appl Math, 1991, 12: 293-326
14. Zheng J L, Zheng X G. A martingale approach to Q-processes, Kexue Tongbao, 1986, 31: 1296-1298
15. Eizenberg A, Freidlin M I. Large deviations for Markov processes corresponding to PDE systems. Ann Probab, 1993, 21: 1015-1044
16. Chow Y S, Teicher H. Probability Theory. New York: Springer-Verlag, 1978
17. Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability. Berlin: Springer-Verlag, 1993
18. Ichihara K, Kunita H. A classification of the second order degenerate elliptic operators and its probabilistic characterization. Z Wahr Verw Geb, 1974, 30: 235-254;
19. 1977, 39: 81-84
20. Kliemann W. Recurrence and invariant measures for degenerate diffusions. Ann Probab, 1987, 15: 690-707
21. Kliemann W. Qualitative theory of stochastic dynamical systems-Applications to life sciences. Bull Math Biol, 1983, 45: 483-506
22. Ehrhardt M. Invariant probabilities for systems in random environment with applications to the Brusselator. Bull Math Biol, 1983, 45: 579-590
23. Meyn S P, Tweedie R L. Stability of Markovian processes II: Continuous time processes and sampled chains. Adv Appl Probab, 1993, 25: 487-517
24. Kunita H. Supports of diffusion processes and controllability problems, In: Itô K, ed. Proc. Internat. Symp. Stochastic Differential Equations. New York: Wiley, 1978, pp. 163-185
25. Meyn S P, Tweedie R L. Stability of Markovian processes I: Discrete time chains. Adv Appl Probab, 1992, 24: 542-574
26. Eizenberg A, Freidlin M I. On the Dirichlet problems for a class of second order PDE systems with small parameter. Stochastics Stochastics Rep, 1990, 33: 111-148
27. Eizenberg A, Freidlin M I. Averaging principle for perturbed random evolution equations and corresponding Dirichlet problems. Probab Theory Relat Fields, 1993, 94: 335-374