Malliavin calculus for Lévy processes with arbitrary Lévy measures
Анотація
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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