Weak convergence to a Markov process: The martingale approach
type: Item
instance of: scholarly article
title: Weak convergence to a Markov process: The martingale approach
zbMATH Open document ID: 0794.60074
DOI: 10.1007/BF01292676
author: Abhay G. Bhatt
author: Rajeeva L. Karandikar
publication date: 1994-08-15T00:00:00Z
review text: We obtain some sufficient conditions for weak convergence of a sequence of processes \(\{X_ n\}\) to \(X\), when \(X\) arises as a solution to a well posed martingale problem. These conditions are tailored for application to the case when the state space for the processes \(X_ n\), \(X\) is infinite-dimensional. The usefulness of these conditions is illustrated by deriving Donsker's invariance principle for Hilbert space valued random variables. Also, continuous dependence of Hilbert space valued diffusions on diffusion and drift coefficients is proved.
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G05
zbMATH DE Number: 569081
zbMATH Keywords: weak convergence
zbMATH Keywords: martingale problem
zbMATH Keywords: Donsker's invariance principle
zbMATH Keywords: Hilbert space valued diffusions
MaRDI profile type: Publication
cites work: Invariant measures and evolution equations for Markov processes characterized via martingale problems
cites work: Q3721531
cites work: The invariance principle for Banach space valued random variables
cites work: Q5533878
cites work: Q3862204
cites work: Q4766372
full work available at URL: https://doi.org/10.1007/bf01292676
OpenAlex ID: W2057919426
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569081