Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps

Yasushi Ishikawa and Hiroshi Kunita

Stochastic Processes and their Applications, 2006, vol. 116, issue 12, 1743-1769

Abstract: We study the existence and smoothness of densities of laws of solutions of a canonical stochastic differential equation (SDE) driven by a Lévy process through the Malliavin calculus on the Wiener-Poisson space. Our assumption needed for the equation is very simple, since we are considering the canonical SDE. Assuming that the Lévy process is nondegenerate, we prove the existence of a smooth density in the case where the coefficients of the equation are nondegenerate. Our main result is stated in Theorem 1.1.

Keywords: Malliavin; calculus; Jump; process; Canonical; process; Density; function (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (12)

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