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EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS

STEVAN PILIPOVIĆ

Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia

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and

DORA SELEŠI

Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia

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https://doi.org/10.1142/S0219025707002634Cited by:26 (Source: Crossref)

Abstract

A new Gel'fand triple exp(S)₁ ⊆ (L)² ⊆ exp(S)_-1 is constructed as extension of the known Kondratiev one (S)₁ ⊆ (L)² ⊆ (S)_-1. Expansion theorems for generalized stochastic processes considered as elements of the spaces and are derived. This series expansion is used for solving a class of evolution stochastic differential equations. The Wick product is developed on the spaces exp(S)_-1, and . The series expansion of generalized stochastic processes is used for solving a class of nonlinear stochastic differential equations by means of Wick products.

Keywords:

AMSC: 60G20, 60H40, 60H30, 46N30, 46F25, 46F10

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