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تسجيل مستخدم جديدMalliavin calculus and Clark-Ocone formula for functionals of a square-integrable Levy process
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In this paper, we construct a Malliavin derivative for functionals of square-integrable Levy processes and derive a Clark-Ocone formula. The Malliavin derivative is defined via chaos expansions involving stochastic integrals with respect to Brownian motion and Poisson random measure. As an illustration, we compute the explicit martingale representation for the maximum of a Levy process.
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An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional expectations of Malli
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In a 2006 article (cite{A1}), Allouba gave his quadratic covariation differentiation theory for It^os integral calculus. He defined the derivative of a semimartingale with respect to a Brownian motion as the time derivative of their quadratic covaria
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