Asymptotic theory of noncentered mixing stochastic differential equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:114

Article

Kim, JH

关键词: diffusion limit;    strong mixing;    Kolmogorov-Fokker-Planck equation;    path integral;   

DOI  :  10.1016/j.spa.2004.05.004

来源: Elsevier

【 摘 要 】

The corrected diffusion effects caused by a noncentered stochastic system are studied in this paper. A diffusion limit theorem or CLT of the system is derived with the convergence error estimate. The estimate is obtained for large t (on the interval (0,t*), t* of the order of epsilon(-1)). The underlying stochastic processes of rapidly varying stochastic inputs are assumed to satisfy a strong mixing condition. The Kolmogorov-Fokker-Planck equation is derived for the transition probability density of the solution process. The result is an extension of the author's previous work [J. Math. Phys. 37 (1996) 752] in that the present system is a noncentered stochastic system on the asymptotically unbounded interval. Furthermore, the solutions of the Kolmogorov-Fokker-Planck equation are represented by an explicit approximate form based upon the pseudodifferential operator theory and Wiener's path integral representation. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free