Abstract
In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration is used. Sufficient conditions for the existence of strong solution to the class of perturbed stochastic Volterra Equations of convolution type are given. Regularity of stochastic convolution is supplied, as well.
Highlights
H, ⋅ H be a seperable Hilbert space and let Ω,( )t≥0, P denote a probability space
The goal of this paper is to formulate sufficient conditions for the existence and regularity of strong solutions to the perturbed Volterra Equation driven by series of scalar Wiener processes
The stochastic integral used in this paper, originally introduced in [5], bases on the construction directly in terms of the sequence of independent scalar processes
Summary
H, ⋅ H be a seperable Hilbert space and let Ω, ,( )t≥0 , P denote a probability space. (2015) A Series Approach to Perturbed Stochastic Volterra Equations of Convolution Typ. Advances in Pure Mathematics, 5, 660-671. The goal of this paper is to formulate sufficient conditions for the existence and regularity of strong solutions to the perturbed Volterra Equation driven by series of scalar Wiener processes. In [1]-[4], the stochastic integral for Hilbert-Schmidt operator-valued integrands and Wiener processes with values in Hilbert space has been constructed. By R (t ), t ≥ 0 , we shall denote the family of resolvent operators corresponding to the Volterra Equation (2), which is defined as follows. The following result concerning convergence of resolvents for the Equation (1) will play the key role. The Equation (2) admits a resolvent tionally, there exists bounded operators An and corresponding resolvent families.
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