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Stochastic Integration with respect to Volterra processes

Abstract : We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which are natural generalization of fractional Brownian motion, we construct a stochastic integral and show some of its main properties: regularity with respect to time and kernel, transformation under an absolutely continuous change of probability, possible approximation schemes and Itô formula.
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https://hal.archives-ouvertes.fr/hal-00358143
Contributor : Laurent Decreusefond Connect in order to contact the contributor
Submitted on : Monday, February 2, 2009 - 9:29:12 PM
Last modification on : Friday, April 23, 2021 - 3:28:03 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 7:58:30 PM

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Laurent Decreusefond. Stochastic Integration with respect to Volterra processes. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2005, 41, pp.123-149. ⟨hal-00358143⟩

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