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A Series Approach to Perturbed Stochastic Volterra Equations of Convolution Type
Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Zielona Góra, Poland
Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Zielona Góra, Poland
- 1 Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Zielona Góra, Poland
- 2 Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Zielona Góra, Poland
Advances in Pure Mathematics·Volume 05 (2015)·Pages 660–671·Published 7 September 2015·DOI10.4236/apm.2015.511060
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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.
KeywordsStochastic Linear Volterra EquationPerturbed EquationStrong SolutionResolventMild SolutionStochastic ConvolutionSeries Approach
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