Про стохастичне інтегрування, диференціювання та віківське числення в аналізі білого шуму Леві

Abstract

The paper is a survey of some author’s results related to the development of the Lévy white noise analysis in terms of Lytvynov’s general- ization of the chaotic representation property, which is an analog of decom- position of square integrable random variables by the Hermite orthogonal polynomials in the Gaussian analysis. Namely with this approach a signifi- cant part of definitions and statements are quite similar to their prototypes from the Gaussian white noise analysis, which is very convenient for possible applications. The survey covers a fairly wide range of issues: constructions of spaces of regular and nonregular test and generalized functions; an extended stochastic integral, a Hida stochastic derivative and operators of stochastic differentiations on different spaces; elements of a Wick calculus; etc.