Seminar to be held in Room 107, 24 Hillhouse at 4:15 pm
Some Aspects of the Anticipating Calculus for the Poisson Process
Abstract: We use the Poisson-Ito chaos decomposition approach to define a
variational derivative operator and its adjoint, which is an anticipating
integral, i.e., agrees with the martingale Poisson-Ito integral with
respect to the compensated Poisson process for predictable integrands.
In the case where the basic probability space is the canonical Poisson
space, our derivative operator is egual to the Carlen and Pardoux gradient
operator that is defined by means of variation of the jump times.