Venerdi 26 ottobre, alle ore 15, il prof. Vlad Bally (UNiversita' Marne La Vallee) terra' un seminario dal titolo "Malliavin Calculus in a weak sense and applications to diffusions with jumps". Il seminario si svolgera' nella SALA DEI SEMINARI del Dipartimento di Matematica, abstract. 1 Malliavin calculus in a weak sense and appli- cations to di¤usions with jumps We present an abstract version of Malliavin calculus. A speci.c point is that we do no more approximate general functionals with simple functionals in L2 sens but in law. This permits to treat problems which are out of rich for the standard calculus. We present the following application. We consider the equation Xt = x + Z t 0 ZR Z 1 0 c(z;Xs)1fu<(Xs;zgdN(s; z; u) where N is a Poisson point measure of intensity measure dsdzdu1u>0: The in.nitesimal operator of this Markov process is Kf(x) = RR(f(x + c(z; x)) f(x))(x; z)dz: Under appropriate hypothesis we prove that the law of Xt is absolutely continuous with respect to the Lebesgue measure and has a smooth density. Notice that the coe¢ cient in the equation is discontinuous and so the standard Malliavin calculus for Poisson point processes, as it is stated in Bichteler Gravereux Jacod, does not apply. 1 _______________________________________________ Settimanale mailing list Settimanale@mail.dm.unipi.it https://mail.dm.unipi.it/mailman/listinfo/settimanale