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July, 1986 Representation Previsible et Changement de Temps
Christophe Stricker
Ann. Probab. 14(3): 1070-1074 (July, 1986). DOI: 10.1214/aop/1176992460


This paper deals with predictable representation and time changed processes. Let $(M^i)_{i\geq 0}$ be a sequence of independent local martingales. Suppose that each $M^i$ has the property of predictable representation with respect to its natural filtration. Suppose also that $(A^i)_{i\geq 1}$ is a sequence of continuous, increasing, $(\mathscr{F}^{M^0}_t)$ adapted processes. We study sufficient conditions in order that $M = M^0 + \sum M^i_{A^i}$ be a local martingale and $M$ have the property of predictable representation with respect to the filtration $(\mathscr{F}^{M^0}_t) \vee (\mathscr{F}^{M^1_{A^1}}_t \vee (\mathscr{F}^{M^2_{A^2}}_t \vee \cdots$. Such problems arise in the modeling of a security market with continuous trading [1].


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Christophe Stricker. "Representation Previsible et Changement de Temps." Ann. Probab. 14 (3) 1070 - 1074, July, 1986.


Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0603.60038
MathSciNet: MR841606
Digital Object Identifier: 10.1214/aop/1176992460

Primary: 60G44
Secondary: 60H05

Keywords: representation of martingales , Semimartingale , stochastic integral , time changed processes

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 3 • July, 1986
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