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- Title
Application of the lent particle method to Poisson-driven SDEs.
- Authors
Bouleau, Nicolas; Denis, Laurent
- Abstract
We apply the Dirichlet form theory to stochastic differential equations with jumps as extension of Malliavin calculus reasoning. As in the continuous case, this weakens significantly the assumptions on the coefficients of the SDE. Thanks to the flexibility of the Dirichlet forms language, this approach brings also an important simplification which was neither available nor visible previously: an explicit formula giving the carré du champ matrix, i.e., the Malliavin matrix. Following this formula a new procedure appears, called the lent particle method which shortens the computations both theoretically and in concrete examples. In this paper which uses the construction done in Bouleau and Denis (J. Funct. Analysis 257:1144-1174, 2009) we restrict ourselves to the existence of densities; smoothness will be studied separately.
- Subjects
NUMERICAL solutions to stochastic differential equations; POISSON processes; MALLIAVIN calculus; DIRICHLET forms; MATHEMATICAL formulas; SMOOTHNESS of functions
- Publication
Probability Theory & Related Fields, 2011, Vol 151, Issue 3/4, p403
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-010-0303-x