Stochastic Equations with an Unbounded Operator Coefficient and Multiplicative Noise
- Authors: Melnikova I.V.1, Alshanskiy M.A.2
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Affiliations:
- Institute of Natural Sciences and Mathematics
- Institute of Radio Engineering and Information Technologies
- Issue: Vol 58, No 6 (2017)
- Pages: 1052-1066
- Section: Article
- URL: https://journal-vniispk.ru/0037-4466/article/view/171591
- DOI: https://doi.org/10.1134/S0037446617060143
- ID: 171591
Cite item
Abstract
Under study is a stochastic operator-differential equation with multiplicative noise in the space of Hilbert-valued generalized random variables. Existence and uniqueness of solutions to the Cauchy problem are proved for the case of an unbounded operator coefficient at the white noise. The equation of population dynamics with a stochastically perturbed multiplication operator is presented as an example.
About the authors
I. V. Melnikova
Institute of Natural Sciences and Mathematics
Author for correspondence.
Email: Irina.Melnikova@urfu.ru
Russian Federation, Ekaterinburg
M. A. Alshanskiy
Institute of Radio Engineering and Information Technologies
Email: Irina.Melnikova@urfu.ru
Russian Federation, Ekaterinburg
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