Articlebronze2006

Malliavin calculus for Lévy processes with arbitrary Lévy measures

21 citations0/0 files storedTheory of Probability and Mathematical Statistics

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

A new method is proposed to prove the absolute continuity of distributions of solutions of stochastic differential equations with jumps. The method is based on the differentiation in time in the space of functionals of the Poisson point measure. In contrast to the known Bismut and Picard methods, our approach can be applied to point measures with arbitrary Lévy measures. We obtain sufficient conditions for the absolute continuity of the solutions expressed in terms of the coefficients of the equation; the conditions do not involve assumptions on properties of the Lévy measure.

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1991Malliavin calculus for processes with jumps 1996On the existence of smooth densities for jump processes 1986Simplified malliavin calculus 1983Calcul des variations stochastique et processus de sauts 1993Integration by Parts for Poisson Processes 2011ON THE SMOOTHNESS OF PDF OF SOLUTIONS TO SDE OF JUMP TYPE

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