Regularity of stochastic Volterra equations by functional calculus methods

We establish pathwise continuity properties of solutions to a stochastic Volterra equation with an additive noise term given by a local martingale. The deterministic part is governed by an operator with an H∞-calculus and a scalar kernel. The proof relies on the dilation theorem for positive definite operator families on a Hilbert space.

An analytic semigroup approach to convolution Volterra equations