Osaka Journal of Mathematics

The Itô-Ventzell formula and forward stochastic differential equations driven by Poisson random measures

Bernt Øksendal and Tusheng Zhang

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Abstract

In this paper we obtain existence and uniqueness of solutions of forward stochastic differential equations driven by compensated Poisson random measures. To this end, an Itô-Ventzell formula for jump processes is proved and the flow properties of solutions of stochastic differential equations driven by compensated Poisson random measures are studied.

Article information

Source
Osaka J. Math., Volume 44, Number 1 (2007), 207-230.

Dates
First available in Project Euclid: 19 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1174324333

Mathematical Reviews number (MathSciNet)
MR2313037

Zentralblatt MATH identifier
1118.60052

Subjects
Primary: 60H40: White noise theory
Secondary: 60G51: Processes with independent increments; Lévy processes 60G57: Random measures 60H07: Stochastic calculus of variations and the Malliavin calculus

Citation

Øksendal, Bernt; Zhang, Tusheng. The Itô-Ventzell formula and forward stochastic differential equations driven by Poisson random measures. Osaka J. Math. 44 (2007), no. 1, 207--230. https://projecteuclid.org/euclid.ojm/1174324333


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