Application of the lent particle method to Poisson driven SDE's

Nicolas Bouleau; Laurent Denis

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arXiv · 0904.3613

Application of the lent particle method to Poisson driven SDE's

Nicolas Bouleau·Laurent Denis

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Abstract

We apply the Dirichlet forms version of Malliavin calculus to stochastic differential equations with jumps. As in the continuous case this weakens significantly the assumptions on the coefficients of the SDE. In spite of the use of the Dirichlet forms theory, this approach brings also an important simplification which was not available nor visible previously : an explicit formula giving the carr\'e 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.

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Nicolas Bouleau, Laurent Denis. 2009-04-23. Application of the lent particle method to Poisson driven SDE's. https://arxiv.org/abs/0904.3613

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