Recurrence and ergodicity of diffusions

R. N. Bhattacharya, S. Ramasubramanian

Research output: Contribution to journalArticle

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

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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