Dyriv M.M.

Operators of Stochastic Differentiation on Spaces of Regular Test and Generalized Functions in the Lévy White Noise Analysis

The operators of stochastic differentiation, which are closely related with stochastic integrals and with the Hida stochastic derivative, play an important role in the classical white noise analysis. In particular, one can use these operators in order to study properties of solutions of normally ordered stochastic equations, and properties of the extended Skorohod stochastic integral. So, it is natural to introduce and to study analogs of the mentioned operators in the Lévy white noise analysis.

Stochastic Integrals with Respect to a Lévy Process and Stochastic Derivatives on Spaces of Regular Test and Generalized Functions

The extended (Skorohod) stochastic integral with respect to a Lévy process and the corresponding Hida stochastic derivative on the space of square integrable random variables (L2) have many applications in the stochastic analysis, in particular, in the theory of stochastic differential and integral equations. But sometimes (for example, in order to consider so-called normally ordered stochastic equations) it is convenient to introduce and study these operators on certain spaces of test and generalized functions or on spaces of some riggings of (L2).