The Annals of Probability

On the Representation of Semimartingales

Hans Follmer

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Abstract

We show that $L^1$-bounded semimartingales (quasi-martingales, $F$-processes) correspond to finite signed measures on the $\sigma$-field of previsible sets. This representation of semimartingales as signed measures is used to derive in a unified manner the main decomposition theorems for semi- and supermartingales.

Article information

Source
Ann. Probab., Volume 1, Number 4 (1973), 580-589.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996887

Digital Object Identifier
doi:10.1214/aop/1176996887

Mathematical Reviews number (MathSciNet)
MR353446

Zentralblatt MATH identifier
0265.60044

JSTOR
links.jstor.org

Subjects
Primary: 60G45

Keywords
Semimartingales (quasi-martingales $F$-processes) as signed measures Rao decomposition Doob-Meyer decomposition Ito-Watanabe factorization

Citation

Follmer, Hans. On the Representation of Semimartingales. Ann. Probab. 1 (1973), no. 4, 580--589. doi:10.1214/aop/1176996887. https://projecteuclid.org/euclid.aop/1176996887


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