A Series Approach to Perturbed Stochastic Volterra Equations of Convolution Type


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.

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Karczewska, A. and Bandrowski, B. (2015) A Series Approach to Perturbed Stochastic Volterra Equations of Convolution Type. Advances in Pure Mathematics, 5, 660-671. doi: 10.4236/apm.2015.511060.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Da Prato, G. and Zabczyk, J. (1992) Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge.
[2] Karczewska, A. (2007) Properties of Convolutions Arising in Stochastic Volterra Equations. International Journal of Contemporary Mathematical Sciences, 2, 1037-1051.
[3] Karczewska, A. (2007) Convolution Type Stochastic Volterra Equations. Lecture Notes in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies. 10. Toruń.
[4] Karczewska, A. and Lizama, C. (2009) Strong Solutions to Stochastic Volterra Equations. Journal of Mathematical Analysis and Applications, 349, 301-310.
[5] van Gaans, O. (2005) A Series Approach to Stochastic Differential Equations with Infinite Dimensional Noise. Integral Equations and Operator Theory, 51, 435-458.
[6] Karczewska, A. and Lizama, C. (2014) Stochastic Volterra Equations under Perturbations. Electronic Communications in Probability, 19, 1-14.
[7] Da Prato, G. and Grisvard, P. (1979) Equations d’volution abstraites non linaires de type parabolique. Annali di Matematica Pura ed Applicata, 120, 329-396.
[8] Ichikawa, A. (1982) Stability of Semilinear Stochastic Evolution Equations. Journal of Mathematical Analysis and Applications, 90, 12-44.

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