On some property of the stochastic derivative operator

Author: Omar Purtukhia
Co-authors: Omar Glonti, Vakhtang Jaoshvili
Keywords: multiple stochastic integral, Skorokhod integral, Malliavin derivative, stochastic derivative operator, Sobolev’s average operator.
Annotation:

We offer a method of finding of kernels of multiple stochastic integrals in chaotic decomposition of “average” stochastic process; we proof that if the square integrable random process is not stochastic differentiable, then the "average" process also is not stochastic differentiable; the rule of stochastic differentiation of a composite function is obtained and property of a commutativity of the stochastic derivative operator and the Sobolev’s average operator is proved.

Lecture files:

On some property of the stochastic derivative operator [en]
სტოქასტური გაწარმოების ოპერატორის ზოგიერთი თვისების შესახებ [ka]