Stochastic Volterra equations with H\"older diffusion coefficients

TL;DR

This paper proves the existence, uniqueness, and regularity properties of solutions to one-dimensional stochastic Volterra equations with H"older continuous diffusion coefficients, expanding understanding of their behavior and properties.

Contribution

It establishes strong solutions and pathwise uniqueness for equations with H"older continuous diffusion coefficients and analyzes their sample path regularity and semimartingale properties.

Findings

Existence of strong solutions confirmed.

Pathwise uniqueness established.

Solutions exhibit specific regularity and semimartingale properties.

Abstract

The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{\"o}lder continuous diffusion coefficients and sufficiently regular kernels. Moreover, we study the sample path regularity, the integrability and the semimartingale property of solutions to one-dimensional stochastic Volterra equations.