The Annals of Probability

Random Time Changes and Convergence in Distribution Under the Meyer-Zheng Conditions

Thomas G. Kurtz

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Abstract

An analog of conditions of Meyer and Zheng for the relative compactness (in the sense of convergence in distribution) of a sequence of stochastic processes is formulated for general separable metric spaces and the corresponding notion of convergence is characterized in terms of the convergence in the Skorohod topology of time changes of the original processes. In addition, convergence in distribution under the topology of convergence in measure is discussed and results of Jacod, Memin and Metivier on convergence under the Skorohod topology are extended.

Article information

Source
Ann. Probab., Volume 19, Number 3 (1991), 1010-1034.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990333

Digital Object Identifier
doi:10.1214/aop/1176990333

Mathematical Reviews number (MathSciNet)
MR1112405

Zentralblatt MATH identifier
0742.60036

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G99: None of the above, but in this section

Keywords
Weak convergence tightness time change Skorohod topology conditional variation

Citation

Kurtz, Thomas G. Random Time Changes and Convergence in Distribution Under the Meyer-Zheng Conditions. Ann. Probab. 19 (1991), no. 3, 1010--1034. doi:10.1214/aop/1176990333. https://projecteuclid.org/euclid.aop/1176990333


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