Convergence of Continuous Stochastic Processes on Compact Metric Spaces Converging in the Lipschitz Distance

Kohei Suzuki

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a new distance, a Lipschitz–Prokhorov distancedLP, on the set Pℳ of isomorphism classes of pairs (X, P) where X is a compact metric space and P is the law of a continuous stochastic process on X. We show that (Pℳ, dLP) is a complete metric space. For Markov processes on Riemannian manifolds, we study relative compactness and convergence.

Original languageEnglish
Pages (from-to)197-219
Number of pages23
JournalPotential Analysis
Volume50
Issue number2
DOIs
Publication statusPublished - 2019 Feb 15

Keywords

  • Lipschitz convergence
  • Markov processes
  • Riemannian manifolds
  • Weak convergence

ASJC Scopus subject areas

  • Analysis

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