On averaging principle for diffusion processes with null-recurrent fast component

R. Khasminskii; N. Krylov

doi:10.1016/S0304-4149(00)00097-1

On averaging principle for diffusion processes with null-recurrent fast component

R. Khasminskii
, N. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

An averaging principle is proved for diffusion processes of type (X_ε(t),Y_ε(t)) with null-recurrent fast component X_ε(t). In contrast with positive recurrent setting, the slow component Y_ε(t) alone cannot be approximated by diffusion processes. However, one can approximate the pair (X_ε(t),Y_ε(t)) by a Markov diffusion with coefficients averaged in some sense.

Original language	English (US)
Pages (from-to)	229-240
Number of pages	12
Journal	Stochastic Processes and their Applications
Volume	93
Issue number	2
DOIs	https://doi.org/10.1016/S0304-4149(00)00097-1
State	Published - Jun 2001

Keywords

Arcsine law
Averaging principle
Homogenization
Null-recurrent diffusion
Primary 60J60
Secondary 60B10

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10.1016/S0304-4149(00)00097-1

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abstract = "An averaging principle is proved for diffusion processes of type (Xε(t),Yε(t)) with null-recurrent fast component Xε(t). In contrast with positive recurrent setting, the slow component Yε(t) alone cannot be approximated by diffusion processes. However, one can approximate the pair (Xε(t),Yε(t)) by a Markov diffusion with coefficients averaged in some sense.",

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AU - Krylov, N.

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AB - An averaging principle is proved for diffusion processes of type (Xε(t),Yε(t)) with null-recurrent fast component Xε(t). In contrast with positive recurrent setting, the slow component Yε(t) alone cannot be approximated by diffusion processes. However, one can approximate the pair (Xε(t),Yε(t)) by a Markov diffusion with coefficients averaged in some sense.

KW - Arcsine law

KW - Averaging principle

KW - Homogenization

KW - Null-recurrent diffusion

KW - Primary 60J60

KW - Secondary 60B10

UR - https://www.scopus.com/pages/publications/0010922516

UR - https://www.scopus.com/pages/publications/0010922516#tab=citedBy

U2 - 10.1016/S0304-4149(00)00097-1

DO - 10.1016/S0304-4149(00)00097-1

M3 - Article

AN - SCOPUS:0010922516

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VL - 93

SP - 229

EP - 240

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

On averaging principle for diffusion processes with null-recurrent fast component

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Keywords

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