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].
Publié le : 1986-07-14
Classification:
Semimartingale,
stochastic integral,
representation of martingales,
time changed processes,
60G44,
60H05
@article{1176992460,
author = {Stricker, Christophe},
title = {Representation Previsible et Changement de Temps},
journal = {Ann. Probab.},
volume = {14},
number = {4},
year = {1986},
pages = { 1070-1074},
language = {fr},
url = {http://dml.mathdoc.fr/item/1176992460}
}
Stricker, Christophe. Representation Previsible et Changement de Temps. Ann. Probab., Tome 14 (1986) no. 4, pp. 1070-1074. http://gdmltest.u-ga.fr/item/1176992460/