On poisson equation and diffusion approximation 2

Annals of Probability

Volumn 31, Issue 3, 2003, Pages 1166-1192

  Pardoux, E ^a,b,c   Veretennikov, A Yu ^a,b,c  

^a UNIVERSITÉ DE PROVENCE   (France)

^b UNIVERSITY OF LEEDS   (United Kingdom)

^c INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

Diffusion approximation; Green function with parameter; Invariant density with parameter; Poisson equation with parameter

Indexed keywords

EID: 0038336352     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1055425774     Document Type: Article

References (17)

1. BAKHVALOV, N. S. (1974). Averaged characteristics of bodies with periodic structure. Soviet Phys. Dokl. 19 650-651. [Translated from Dokl. Akad. Nauk SSSR 218 (1974) 1046-1048.]
2. BAKHVALOV, N. S. (1975). Averaging of partial differential equations with rapidly oscillating coefficients. Sov. Math. Dokl. 16 351-355. [Translated from Dokl. Akad. Nauk SSSR 221 (1975) 516-519.]
3. BENVENISTE, A., METIVIER, M. and PRIOURET, P. (1987). Algorithmes adaptifs et approximations stochastiques. Théorie et applications à l'identification, au traitment du signal et à reconnaissance des formes. Masson, Paris. [English translation (1990) Adaptive Algorithms and Stochastic Approximations. Springer, Berlin.]
4. EIDELMAN, S. D. (1956). On the fundamental solutions of parabolic systems. Soviet Math. Sbornik 38 51-92. [English translation Amer. Math. Soc. Transl. 41 (1964) 1-48.]
5. EIDELMAN, S. D. (1964). Parabolic Systems. Nauka, Moscow (in Russian).
6. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes. Characterization and Convergence. Wiley, New York.
7. FREIDLIN, M. I. and WENTZELL, S. D. (1984). Random Perturbations of Dynamical Systems. Springer, New York.
8. FRIEDMAN, A. (1964) Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, NJ.
9. GLYNN, P. W. and MEYN, S. P. (1996). A Liapounov bound for solutions of the Poisson equation. Ann. Probab. 24 916-931.
10. KIFER, YU. (2001). Averaging and climate models. In Stochastic Climate Models (P. Imkeller and J. von Stroch, eds.). Birkhäuser, Basel.
11. KRYLOV, N. V. (1980). Controlled Diffusion Processes. Springer, Berlin.
12. LADYZENSKAJA, O., SOLONNIKOV, V. and URAL'CEVA, N. (1968). Linear and Quasilinear Equations of Parabolic Type. Amer. Math. Soc., Providence, RI.
13. PAPANICOLAOU, G. C., STROOCK, D. W. and VARADHAN, S. R. S (1976). Martingale approach to some limit theorems. In Statistical Mechanics and Dynamical Systems (D. Ruelle ed.) 1-12. Duke Univ. Math. Series 3.
14. PARDOUX, É. and VERETENNIKOV, A. YU. (2000). On regularity of an invariant density of a Markov chain in a parameter, Russian Math. Dokl. 370 158-160.
15. PARDOUX, É. and VERETENNIKOV, A. YU. (2001). On Poisson equation and diffusion approximation 1. Ann. Probab. 29 1061-1085.
16. VERETENNIKOV, A. Yu. (1997). On polynomial mixing bounds for stochastic differential equations. Stock. Processes Appl. 70 115-127.
17. VERETENNIKOV, A. YU. (1999). On polynomial mixing and convergence rate for stochastic difference and differential equations. Teor. Veroyatnost. i Primenen. 44 312-327 (in Russian). [English translation Theory Probab. Appl. 44 (2000) 361-374.]