On the Analysis of a Singular Stochastic Volterra Differential Equation driven by a Wiener Noise

TL;DR

This paper constructs unique strong solutions for a class of singular stochastic Volterra differential equations driven by Wiener noise and investigates their Sobolev differentiability with respect to initial conditions.

Contribution

It introduces a method to establish existence and uniqueness of solutions for singular stochastic Volterra equations and analyzes their differentiability properties.

Findings

Established existence and uniqueness of strong solutions.

Proved Sobolev differentiability of solutions with respect to initial data.

Analyzed the impact of singular drift on solution behavior.

Abstract

In this article, we construct unique strong solutions to a class of stochastic Volterra differential equations driven by a singular drift vector field and a Wiener noise. Further, we examine the Sobolev differentiability of the strong solution with respect to its initial value.