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 \({H^\infty}\)-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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Dedicated to Jan Prüss, in admiration of his unfaltering spirit and his outstanding mathematical work.
Mark Veraar author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organization for Scientific Research (NWO).
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Schnaubelt, R., Veraar, M. Regularity of stochastic Volterra equations by functional calculus methods. J. Evol. Equ. 17, 523–536 (2017). https://doi.org/10.1007/s00028-016-0365-z
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DOI: https://doi.org/10.1007/s00028-016-0365-z