Asymptotic theory of noncentered mixing stochastic differential equations

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 [var 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.