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

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