Convolution type stochastic Volterra equations

Abstract

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.

Monograph, 101 pages

References in corpus (1)

• Stochastic Integral with respect to Cylindrical Wiener Process

Cited by in corpus (5)

• Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise
• Non-linear noise excitation for some space-time fractional stochastic equations in bounded domains
• Langevin equation and fractional dynamics
• A series approach to stochastic Volterra equations of convolution time
• Temporal and spatial regularity of solutions to stochastic Volterra equations of convolution type