Mittag-Leffler's Function and Stochastic Linear Volterra Equations of Convolution Type

Abstract

We consider the class of stochastic linear Volterra equations of convolution type defined by fractional integration kernels g ρ (t)={ 1 Γ(ρ) }t ρ−1, ρ∈(0,2). Using an explicit formula for the scalar resolvent function, we establish the basic properties of the stochastic convolution process W S . Our formulas are given in terms of the Mittag-Leffler's function