An asymptotic limit law with a singularly perturbed drift and a random noise

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

An asymptotic stochastic initial value problem with a random microscale superposed upon a deterministic macroscale is considered in this article. We derive and prove a limit theorem for the random problem with a rapidly varying deterministic component. The asymptotic character of the stochastic initial value problem with a small parameter is realized by solving a final value problem of which the infinitesimal generator consists of a singularly perturbed deterministic component and a random fluctuation intensity component. We also give an estimate for the error in the asymptotic approximation in terms of the small parameter. This abstract limit theorem is reduced to a limit theorem for the stochastic processes solving a system of stochastic differential equations. The corresponding infinitesimal generator of the Kolmogorov-Fokker-Planck equation is obtained in an asymptotic form and demonstrates how an effective driving force couples with a zero-mean random perturbation in both drift and diffusion coefficients. Our theorem provides a characterization of random noise for evanescent waves in a layered random medium.

Original languageEnglish
Pages (from-to)2660-2675
Number of pages16
JournalJournal of Mathematical Physics
Volume38
Issue number5
DOIs
Publication statusPublished - 1997 May

Fingerprint

Limit Laws
Asymptotic Limit
Random Noise
random noise
Singularly Perturbed
Limit Theorems
theorems
Infinitesimal Generator
Small Parameter
Initial Value Problem
boundary value problems
Evanescent Wave
Kolmogorov Equation
generators
Random Perturbation
Random Media
Asymptotic Approximation
Driving Force
Fokker-Planck Equation
Diffusion Coefficient

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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An asymptotic limit law with a singularly perturbed drift and a random noise. / Kim, Jeong Hoon.

In: Journal of Mathematical Physics, Vol. 38, No. 5, 05.1997, p. 2660-2675.

Research output: Contribution to journalArticle

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