## The Annals of Probability

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60G99: None of the above, but in this section

Secondary: 60J30

**Keywords**

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

#### Citation

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