Abstract semilinear stochastic Itó-Volterra integrodifferential equations

Author:

Keck David N.,McKibben Mark A.ORCID

Abstract

We consider a class of abstract semilinear stochastic Volterra integrodifferential equations in a real separable Hilbert space. The global existence and uniqueness of a mild solution, as well as a perturbation result, are established under the so-called Caratheodory growth conditions on the nonlinearities. An approximation result is then established, followed by an analogous result concerning a so-called McKean-Vlasov integrodifferential equation, and then a brief commentary on the extension of the main results to the time-dependent case. The paper ends with a discussion of some concrete examples to illustrate the abstract theory.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Modelling and Simulation,Statistics and Probability

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise;Journal of Differential Equations;2015-01

2. Bibliography;Chapman & Hall/CRC Applied Mathematics & Nonlinear Science;2011-06-08

3. Controllability of nonlinear impulsive Ito type stochastic systems;International Journal of Applied Mathematics and Computer Science;2009-12-01

4. Asymptotic stability of impulsive stochastic partial differential equations with infinite delays;Journal of Mathematical Analysis and Applications;2009-08

5. Controllability of non-linear impulsive stochastic systems;International Journal of Control;2009-04-08

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