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

Thomas G. Kurtz
The Annals of Probability
Vol. 19, No. 3 (Jul., 1991), pp. 1010-1034
Stable URL: http://www.jstor.org/stable/2244471
Page Count: 25
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Random Time Changes and Convergence in Distribution Under the Meyer-Zheng Conditions
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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.

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