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arXiv · 0805.2084

Stochastic calculus for convoluted Lévy processes

Christian Bender·Tina Marquardt
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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. 2008-05-14. Stochastic calculus for convoluted Lévy processes. https://doi.org/10.3150/07-bej115

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