## The Annals of Probability

### Series of Random Processes without Discontinuities of the Second Kind

Olav Kallenberg

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 2, Number 4 (1974), 729-737.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996615

Digital Object Identifier
doi:10.1214/aop/1176996615

Mathematical Reviews number (MathSciNet)
MR370679

Zentralblatt MATH identifier
0286.60027

JSTOR