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August, 1974 Series of Random Processes without Discontinuities of the Second Kind
Olav Kallenberg
Ann. Probab. 2(4): 729-737 (August, 1974). DOI: 10.1214/aop/1176996615


For series of independent random processes in the space $D\lbrack 0, 1 \rbrack$ endowed with the Skorohod topology, convergence in distribution is shown to imply almost sure convergence. Under mild conditions, such as e.g. when the limiting process has no jumps of fixed size and location, the latter convergence is uniform. As an application, we discuss a representation by Ferguson and Klass of processes with independent increments.


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Olav Kallenberg. "Series of Random Processes without Discontinuities of the Second Kind." Ann. Probab. 2 (4) 729 - 737, August, 1974.


Published: August, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0286.60027
MathSciNet: MR370679
Digital Object Identifier: 10.1214/aop/1176996615

Primary: 60G99
Secondary: 60J30

Keywords: convergence almost surely and in distribution , processes with independent increments , processes without discontinuities of the second kind , Series of random processes , Skorohod and uniform topologies

Rights: Copyright © 1974 Institute of Mathematical Statistics

Vol.2 • No. 4 • August, 1974
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