## The Annals of Probability

### Representation Previsible et Changement de Temps

Christophe Stricker

#### Abstract

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].

#### Article information

Source
Ann. Probab., Volume 14, Number 3 (1986), 1070-1074.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992460

Digital Object Identifier
doi:10.1214/aop/1176992460

Mathematical Reviews number (MathSciNet)
MR841606

Zentralblatt MATH identifier
0603.60038

JSTOR

Subjects
Primary: 60G44: Martingales with continuous parameter
Secondary: 60H05: Stochastic integrals

#### Citation

Stricker, Christophe. Representation Previsible et Changement de Temps. Ann. Probab. 14 (1986), no. 3, 1070--1074. doi:10.1214/aop/1176992460. https://projecteuclid.org/euclid.aop/1176992460