Convolution type stochastic Volterra equations

Details Convolution type stochastic Volterra equations Convolution type stochastic Volterra equations

2007-12-28

arxiv.org/abs/0712.4357v1

Lecture Notes in Nonlinear Analysis, Juliusz Schauder Center for Nonlinear Studies 10, Torun, 2007

Mathematics

Probability

Monograph, 101 pages

Scientific paper

The aim of this work is to present, in self-contained form, results concerning fundamental and the most important questions related to linear stochastic Volterra equations of convolution type. The paper is devoted to study the existence and some kind of regularity of solutions to stochastic Volterra equations in Hilbert space and the space of tempered distributions, as well. In recent years the theory of Volterra equations, particularly fractional ones, has undergone a big development. This is an emerging area of research with interesting mathematical questions and various important applications. The increasing interest in these equations comes from their applications to problems from physics and engeenering, particularly from viscoelasticity, heat conduction in materials with memory or electrodynamics with memory.

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