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August 2016 Integration theory for infinite dimensional volatility modulated Volterra processes
Fred Espen Benth, André Süss
Bernoulli 22(3): 1383-1430 (August 2016). DOI: 10.3150/15-BEJ696


We treat a stochastic integration theory for a class of Hilbert-valued, volatility-modulated, conditionally Gaussian Volterra processes. We apply techniques from Malliavin calculus to define this stochastic integration as a sum of a Skorohod integral, where the integrand is obtained by applying an operator to the original integrand, and a correction term involving the Malliavin derivative of the same altered integrand, integrated against the Lebesgue measure. The resulting integral satisfies many of the expected properties of a stochastic integral, including an Itô formula. Moreover, we derive an alternative definition using a random-field approach and relate both concepts. We present examples related to fundamental solutions to partial differential equations.


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Fred Espen Benth. André Süss. "Integration theory for infinite dimensional volatility modulated Volterra processes." Bernoulli 22 (3) 1383 - 1430, August 2016.


Received: 1 October 2013; Revised: 1 July 2014; Published: August 2016
First available in Project Euclid: 16 March 2016

zbMATH: 1341.60047
MathSciNet: MR3474820
Digital Object Identifier: 10.3150/15-BEJ696

Keywords: Gaussian random fields , Malliavin calculus , stochastic integration , Volterra processes

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 3 • August 2016
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