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THE ITÔ-VENTZELL FORMULA AND FORWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY POISSON RANDOM MEASURES

19 citations0/0 files storedOsaka City University (Osaka City University)

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

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

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1983Stochastic Differential Equations and Diffusion Processes 2006The Malliavin Calculus and Related Topics 1997Processes of normal inverse Gaussian type 1997Stochastic Analysis 1988Stochastic calculus with anticipating integrands 1997Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach.1993Forward, backward and symmetric stochastic integration 2005Stochastic Integration and Differential Equations. Second Edition.

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