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May 2008 Stochastic calculus for convoluted Lévy processes
Christian Bender, Tina Marquardt
Bernoulli 14(2): 499-518 (May 2008). DOI: 10.3150/07-BEJ115

Abstract

We develop a stochastic calculus for processes which are built by convoluting a pure jump, zero expectation Lévy process with a Volterra-type kernel. This class of processes contains, for example, fractional Lévy processes as studied by Marquardt [Bernoulli 12 (2006) 1090–1126.] The integral which we introduce is a Skorokhod integral. Nonetheless, we avoid the technicalities from Malliavin calculus and white noise analysis and give an elementary definition based on expectations under change of measure. As a main result, we derive an Itô formula which separates the different contributions from the memory due to the convolution and from the jumps.

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Christian Bender. Tina Marquardt. "Stochastic calculus for convoluted Lévy processes." Bernoulli 14 (2) 499 - 518, May 2008. https://doi.org/10.3150/07-BEJ115

Information

Published: May 2008
First available in Project Euclid: 22 April 2008

zbMATH: 1173.60017
MathSciNet: MR2544099
Digital Object Identifier: 10.3150/07-BEJ115

Rights: Copyright © 2008 Bernoulli Society for Mathematical Statistics and Probability

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Vol.14 • No. 2 • May 2008
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