2009/04/23 by Nicolas Bouleau, Bouleau, Nicolas, Laurent Denis +1
Economics, Econometrics and Finance · Physics and Astronomy · #60G51 #60G57 #60H05 #60J45 #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.0904.3613
openalex publication_date 2009/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.