Pathwise uniqueness for singular stochastic Volterra equations with H\"older coefficients

TL;DR

This paper proves pathwise uniqueness and existence of strong solutions for a class of one-dimensional stochastic Volterra equations driven by Brownian motion with singular kernels and H"older continuous coefficients.

Contribution

It establishes pathwise uniqueness and strong solution existence for stochastic Volterra equations with singular kernels and H"older coefficients, extending previous results.

Findings

Pathwise uniqueness is proven for the class of equations.

Existence of unique strong solutions is demonstrated.

Results apply to equations with singular kernels and H"older coefficients.

Abstract

Pathwise uniqueness is established for a class of one-dimensional stochastic Volterra equations driven by Brownian motion with singular kernels and H\"older continuous diffusion coefficients. Consequently, the existence of unique strong solutions is obtained for this class of stochastic Volterra equations.