|
This article is cited in 3 scientific papers (total in 3 papers)
Stochastic equations with an unbounded operator coefficient and multiplicative noise
I. V. Melnikovaa, M. A. Alshanskiyb a Ural Federal University, Institute of Natural Sciences and Mathematics, Ekaterinburg, Russia
b Ural Federal University, Institute of Radio Engineering and Information Technologies, Ekaterinburg, Russia
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.
Keywords:
stochastic operator-differential equation, white noise, generalized random variable, S-transform, Wick product, Hitsuda–Skorokhod integral.
Received: 10.11.2015 Revised: 13.05.2017
Citation:
I. V. Melnikova, M. A. Alshanskiy, “Stochastic equations with an unbounded operator coefficient and multiplicative noise”, Sibirsk. Mat. Zh., 58:6 (2017), 1354–1371; Siberian Math. J., 58:6 (2017), 1052–1066
Linking options:
https://www.mathnet.ru/eng/smj2943 https://www.mathnet.ru/eng/smj/v58/i6/p1354
|
Statistics & downloads: |
Abstract page: | 247 | Full-text PDF : | 59 | References: | 48 | First page: | 7 |
|