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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 6, Pages 90–99
(Mi ivm7508)
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This article is cited in 1 scientific paper (total in 1 paper)
Solution of nonlinear stochastic equations with a generator of a semigroup discontinuous at zero
A. A. Ogorodnikov Chair of Mathematical Analysis, Ural State University, Ekaterinburg, Russia
Abstract:
In this paper we study the Cauchy problem for a nonlinear stochastic equation with a generator of a semigroup discontinuous at zero. We prove the unique existence of a mild solution for some class of such semigroups. We establish a connection between weak and mild solutions for such semigroups.
Keywords:
abstract stochastic Cauchy problem, operator semigroup, $Q$-Wiener process, stochastic integral.
Received: 23.12.2009
Citation:
A. A. Ogorodnikov, “Solution of nonlinear stochastic equations with a generator of a semigroup discontinuous at zero”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 6, 90–99; Russian Math. (Iz. VUZ), 55:6 (2011), 76–84
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https://www.mathnet.ru/eng/ivm7508 https://www.mathnet.ru/eng/ivm/y2011/i6/p90
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Abstract page: | 305 | Full-text PDF : | 86 | References: | 39 | First page: | 5 |
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