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

By Yasushi Ishikawa, Hiroshi Kunita. 2006

102 citations recorded by the source corpus.

We study the existence and smoothness of densities of laws of solutions of a canonical stochastic differential equation (SDE) driven by a Levy 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 Levy 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.

Subfields: Finance, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/e502ff1d654daf3cd0a8cd47f27c455d86c5b73a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Nicolas G. Fournier
2. Vlad Bally
3. Jacques Printems
4. Emmanuelle Clement
5. A. Kulik
6. Huyen Pham
7. René A. Carmona
8. M. Ludkovski

In Mathematical Physics

1. Nicolas G. Fournier
2. Vlad Bally
3. Nicolas Champagnat
4. Viet Chi Tran
5. Arnaud Debussche
6. Bertrand Cloez

Citations in the corpus

• Absolute continuity for some one-dimensional processes (2008, background): “Ishikawa-Kunita [15] have obtained some regularity results under some very simple assumptions for a different type of jumping SDEs, namely canonical SDEs with jumps, see [15, Eq.”
• Integration by parts formula and applications to equations with jumps (2009, background): “[6] much work concerning the Malliavin calculus for Poisson point measures has been done and many different approaches have been developed: see for example [1,8,13,19,21].”