Regularity of stochastic Volterra equations by functional calculus methods

2015/12/08 by Schnaubelt, Roland, Veraar, Mark · 1 citation
#60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 60H20 #Probability (math.PR) #Secondary: 45N05

paper · doi:10.48550/arxiv.1512.02485

Abstract

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.

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