The Annals of Probability

Weak Convergence of Markov Processes with Extended Generators

Aihua Xia

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Abstract

In this article, we give some sufficient conditions for the weak convergence of Markov processes in terms of their extended generators. For the convergence of Markov processes with generators defined by Dynkin, necessary and sufficient conditions are obtained. As an application, we will discuss the convergence of diffusion processes with jumps.

Article information

Source
Ann. Probab. Volume 22, Number 4 (1994), 2183-2202.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176988499

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176988499

Mathematical Reviews number (MathSciNet)
MR1331220

Zentralblatt MATH identifier
0839.60006

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J27: Continuous-time Markov processes on discrete state spaces

Keywords
Shorokhod distance weak convergence tightness Markov process local martingale semigroup resolvent generator diffusion process with jumps

Citation

Xia, Aihua. Weak Convergence of Markov Processes with Extended Generators. The Annals of Probability 22 (1994), no. 4, 2183--2202. doi:10.1214/aop/1176988499. http://projecteuclid.org/euclid.aop/1176988499.


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