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On Generalized Solutions to Stochastic Systems

  • Irina V. MelnikovaEmail author
  • Uliana A. Alekseeva
Part of the Operator Theory: Advances and Applications book series (OT, volume 245)

Abstract

We consider the Cauchy problem for systems of differential equations with white noise type random perturbations. Generalized solutions with respect to spatial variable x of the problem in the Itô statement are obtained in spaces \(\Psi^{\prime}\) depending on a type of the system. Generalized solutions with respect to t and x of the problem in the differential statement are obtained in spaces \(\mathcal{D}^{\prime}\Psi^{\prime}\).

Keywords

Stochastic systems white noise Wiener process distribution spaces regularized semigroup generalized solution 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Ural Federal UniversityEkaterinburgRussia

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