Lp-valued stochastic convolution integral driven by Volterra noise

Convolution spline approximations of Volterra integral equations

We derive a new “convolution spline” approximation method for convolution Volterra integral equations. This shares some properties of convolution quadrature, but instead of being based on an underlying ODE solver is explicitly constructed in terms of basis functions which have compact support. At time step tn = nh > 0, the solution is approximated in a “backward time” manner in terms of basis f...

Stochastic Volterra convolution with Lévy process

In the paper we study stochastic convolution appearing in Volterra equation driven by so called Lévy process. By Lévy process we mean a process with homogeneous independent increments, continuous in probability and cadlag.

Kernel perturbations for convolution first kind Volterra integral equations

Because of their causal structure, (convolution) Volterra integral equations arise as models in a variety of real-world situations including rheological stress-strain analysis, population dynamics and insurance risk prediction. In such practical situations, often only an approximation for the kernel is available. Consequently, a key aspect in the analysis of such equations is estimating the eff...

Stochastic Volterra integral equations with a parameter

A Numerical Method for Solving Stochastic Volterra-Fredholm Integral Equation

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...