On numerical solutions to stochastic Volterra equations

TL;DR

This paper explores the application of the Galerkin method to solve deterministic and stochastic Volterra equations, combining theoretical insights with numerical algorithms and illustrative examples.

Contribution

It introduces a numerical algorithm based on the Galerkin method for solving stochastic Volterra equations, expanding existing techniques.

Findings

Demonstrates the effectiveness of the Galerkin method for stochastic Volterra equations

Provides numerical examples illustrating the method's features

Revisits theoretical results on Volterra equations

Abstract

The aim of the paper is to demonstrate the use of the Galerkin method for some kind of Volterra equations, determininistic and stochastic as well. The paper consists of two parts: the theoretical and numerical one. In the first part we recall some apparently well-known results concerning the Volterra equations under consideration. In the second one we describe a numerical algorithm used and next present some examples of numerical solutions in order to illustrate the pertinent features of the technique used in the paper.