We give the Wiener-Itô chaotic decomposition for the local time of the d-dimensional fractional Brownian motion with N -parameters and study its smoothness in the Sobolev-Watanabe spaces. 384 Eddahbi et al. representation of the form B H t = t 0 386 Eddahbi et al.

We deal with backward stochastic differential equations (BSDE for short) driven by Teugel's martingales and an independent Brownian motion. We study the existence, uniqueness and comparison of solutions for these equations under a Lipschitz as well as a locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we prove that if the Lipschitz constant LN behaves as log(N) in the ball B(0,N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differential integral equations (PDIE for short).

No abstract