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Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  09 April 2009

Zhen Wu
Zhen Wu
Affiliation:
School of Mathematics and System Science Shandong UniversityJinan 250100China e-mail: wuzhen@sdu.edu.cn
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Abstract

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We first give the existence and uniqueness result and a comparison theorem for backward stochastic differential equations with Brownian motion and Poisson process as the noise source in stopping time (unbounded) duration. Then we obtain the existence and uniqueness result for fully coupled forward-backward stochastic differential equation with Brownian motion and Poisson process in stopping time (unbounded) duration. We also proved a comparison theorem for this kind of equation.

Keywords

stochastic differential equationsstopping timerandom measurePoisson processcomparison theorem.

MSC classification

Secondary: 60H10: Stochastic ordinary differential equations 60G40: Stopping times; optimal stopping problems; gambling theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 249 - 266
Copyright
Copyright © Australian Mathematical Society 2003

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