Recurrence and ergodicity of diffusions

Rabindra N Bhattacharya, S. Ramasubramanian

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)95-122
Number of pages28
JournalJournal of Multivariate Analysis
Volume12
Issue number1
DOIs
StatePublished - 1982

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Ergodicity
Recurrence
Lower and Upper Functions
Positive Recurrence
Transience
Functional Central Limit Theorem
Weak Convergence
Asymptotic Properties
Limiting
Sufficient Conditions

Keywords

  • invariant measures
  • space-time harmonic functions
  • Stopping times

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

Recurrence and ergodicity of diffusions. / Bhattacharya, Rabindra N; Ramasubramanian, S.

In: Journal of Multivariate Analysis, Vol. 12, No. 1, 1982, p. 95-122.

Research output: Contribution to journalArticle

Bhattacharya, Rabindra N ; Ramasubramanian, S. / Recurrence and ergodicity of diffusions. In: Journal of Multivariate Analysis. 1982 ; Vol. 12, No. 1. pp. 95-122.
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