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July, 1991 Random Time Changes and Convergence in Distribution Under the Meyer-Zheng Conditions
Thomas G. Kurtz
Ann. Probab. 19(3): 1010-1034 (July, 1991). DOI: 10.1214/aop/1176990333


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.


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Thomas G. Kurtz. "Random Time Changes and Convergence in Distribution Under the Meyer-Zheng Conditions." Ann. Probab. 19 (3) 1010 - 1034, July, 1991.


Published: July, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0742.60036
MathSciNet: MR1112405
Digital Object Identifier: 10.1214/aop/1176990333

Primary: 60F17
Secondary: 60G99

Keywords: conditional variation , Skorohod topology , tightness , Time change , weak convergence

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 3 • July, 1991
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