The Annals of Probability
- Ann. Probab.
- Volume 2, Number 4 (1974), 729-737.
Series of Random Processes without Discontinuities of the Second Kind
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.
Ann. Probab., Volume 2, Number 4 (1974), 729-737.
First available in Project Euclid: 19 April 2007
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Series of random processes processes without discontinuities of the second kind convergence almost surely and in distribution Skorohod and uniform topologies processes with independent increments
Kallenberg, Olav. Series of Random Processes without Discontinuities of the Second Kind. Ann. Probab. 2 (1974), no. 4, 729--737. doi:10.1214/aop/1176996615. https://projecteuclid.org/euclid.aop/1176996615