Recurrence and ergodicity of diffusions

R. N. Bhattacharya; S. Ramasubramanian

doi:10.1016/0047-259X(82)90086-0

Recurrence and ergodicity of diffusions

R. N. Bhattacharya, S. Ramasubramanian

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

13 Scopus citations

Abstract

This article attempts to lay a proper foundation for studying asymptotic properties of nonhomogeneous diffusions, extends earlier criteria for transience, recurrence, and positive recurrence, and provides sufficient conditions for the weak convergence of a shifted nonhomogeneous diffusion to a limiting stationary homogenous diffusion. A functional central limit theorem is proved for the class of positive recurrent homogeneous diffusions. Upper and lower functions for positive recurrent nonhomogeneous diffusions are also studied.

Original language	English (US)
Pages (from-to)	95-122
Number of pages	28
Journal	Journal of Multivariate Analysis
Volume	12
Issue number	1
DOIs	https://doi.org/10.1016/0047-259X(82)90086-0
State	Published - Mar 1982
Externally published	Yes

Keywords

Stopping times
invariant measures
space-time harmonic functions

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/0047-259X(82)90086-0

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title = "Recurrence and ergodicity of diffusions",

abstract = "This article attempts to lay a proper foundation for studying asymptotic properties of nonhomogeneous diffusions, extends earlier criteria for transience, recurrence, and positive recurrence, and provides sufficient conditions for the weak convergence of a shifted nonhomogeneous diffusion to a limiting stationary homogenous diffusion. A functional central limit theorem is proved for the class of positive recurrent homogeneous diffusions. Upper and lower functions for positive recurrent nonhomogeneous diffusions are also studied.",

keywords = "Stopping times, invariant measures, space-time harmonic functions",

author = "Bhattacharya, {R. N.} and S. Ramasubramanian",

note = "Funding Information: Received December 29, 1980; revised May 15, 1981. AMS 1970 subject classification: 60560. Key words and phrases: Stopping times, space-time harmonic functions, invariant measures. * Research of this author was supported by the United States National Science Foundation Grant MCS 79-03004.",

year = "1982",

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doi = "10.1016/0047-259X(82)90086-0",

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volume = "12",

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AU - Bhattacharya, R. N.

AU - Ramasubramanian, S.

N1 - Funding Information: Received December 29, 1980; revised May 15, 1981. AMS 1970 subject classification: 60560. Key words and phrases: Stopping times, space-time harmonic functions, invariant measures. * Research of this author was supported by the United States National Science Foundation Grant MCS 79-03004.

PY - 1982/3

Y1 - 1982/3

N2 - This article attempts to lay a proper foundation for studying asymptotic properties of nonhomogeneous diffusions, extends earlier criteria for transience, recurrence, and positive recurrence, and provides sufficient conditions for the weak convergence of a shifted nonhomogeneous diffusion to a limiting stationary homogenous diffusion. A functional central limit theorem is proved for the class of positive recurrent homogeneous diffusions. Upper and lower functions for positive recurrent nonhomogeneous diffusions are also studied.

AB - This article attempts to lay a proper foundation for studying asymptotic properties of nonhomogeneous diffusions, extends earlier criteria for transience, recurrence, and positive recurrence, and provides sufficient conditions for the weak convergence of a shifted nonhomogeneous diffusion to a limiting stationary homogenous diffusion. A functional central limit theorem is proved for the class of positive recurrent homogeneous diffusions. Upper and lower functions for positive recurrent nonhomogeneous diffusions are also studied.

KW - Stopping times

KW - invariant measures

KW - space-time harmonic functions

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EP - 122

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 1

ER -

Recurrence and ergodicity of diffusions

Abstract

Keywords

ASJC Scopus subject areas

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