Asymptotic theory of noncentered mixing stochastic differential equations

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Abstract

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 ε-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.

Original languageEnglish
Pages (from-to)161-174
Number of pages14
JournalStochastic Processes and their Applications
Volume114
Issue number1
DOIs
Publication statusPublished - 2004 Nov

Bibliographical note

Funding Information:
This work was supported by the interdisciplinary research program of the KOSEF 1999-2-103-001-5 and also by Brain Korea 21 project in 2001. The two referees are thanked for their comments and suggestions on this paper.

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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