An anticipatine stochastic calculus (or Malliavin calculus) with respect to a Levy process will be constructed based on the chaotic decomposition. In particular, the derivation operators and Skorohod integrals with respect the family of normal martingales will be defined. Special interest will devoted to get a Clark-Ocone formula. These results will be applied to Finanze theory since a Levy process is a good model for a marked with jumps. Further, we will study the Malliavin calculus with respect to the fractional brownian motion. Jorward and backward integrals will be defined and related with the known integrals. The solution of a stochastic differential equation perturbed by a fractionary noise will be studied. Stochstic differential equation (driven by a brownian or a Poisson) with conditions on the boundary, will be considered. The Onsager-Machlup functional for a stochastic evolution equation.
|Effective start/end date||19/12/00 → 19/12/03|