Regularity of stochastic Volterra equations by functional calculus methods

Roland Schnaubelt; Mark Veraar

doi:10.1007/s00028-016-0365-z

Regularity of stochastic Volterra equations by functional calculus methods

Roland Schnaubelt, Mark Veraar

Analysis

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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.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Journal of Evolution Equations
DOIs	https://doi.org/10.1007/s00028-016-0365-z
Publication status	Published - 2016

Keywords

Stochastic Volterra equation
Pathwise continuity
Local martingale
Dilation
H∞-calculus

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10.1007/s00028-016-0365-z

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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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KW - Stochastic Volterra equation

KW - Pathwise continuity

KW - Local martingale

KW - Dilation

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JF - Journal of Evolution Equations

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Regularity of stochastic Volterra equations by functional calculus methods

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Keywords

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