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August, 1973 On the Representation of Semimartingales
Hans Follmer
Ann. Probab. 1(4): 580-589 (August, 1973). DOI: 10.1214/aop/1176996887

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.

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Hans Follmer. "On the Representation of Semimartingales." Ann. Probab. 1 (4) 580 - 589, August, 1973. https://doi.org/10.1214/aop/1176996887

Information

Published: August, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0265.60044
MathSciNet: MR353446
Digital Object Identifier: 10.1214/aop/1176996887

Subjects:
Primary: 60G45

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

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 4 • August, 1973
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