207 research outputs found
Asymptotic behaviour of mild solution of nonlinear stochastic partial functional equations
This paper presents conditions to assure existence, uniqueness and stability for impulsive neutral stochastic integrodifferential equations with delay driven by Rosenblatt process and Poisson jumps. The Banach fixed point theorem and the theory of resolvent operator developed by Grimmer [R.C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc., 273(1):333–349, 1982] are used. An example illustrates the potential benefits of these results
Stochastic Volterra equations driven by cylindrical Wiener process
In this paper, stochastic Volterra equations driven by cylindrical Wiener
process in Hilbert space are investigated. Sufficient conditions for existence
of strong solutions are given. The key role is played by convergence of
-times resolvent families.Comment: 14 pages. Sufficient conditions for existence of strong solutions for
stochastic fractional Volterra equations are given. Some proofs precise
Exponential behavior of solutions to stochastic integrodifferential equations with distributed delays
In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C0-semigroup
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