Stochastic Volterra equations with Hölder diffusion coefficients

Abstract

The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{ö}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.

arXiv comment25 pages