• Bernoulli
  • Volume 14, Number 2 (2008), 499-518.

Stochastic calculus for convoluted Lévy processes

Christian Bender and Tina Marquardt

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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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Bernoulli, Volume 14, Number 2 (2008), 499-518.

First available in Project Euclid: 22 April 2008

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convoluted Lévy process fractional Lévy process Itô formula Skorokhod integration


Bender, Christian; Marquardt, Tina. Stochastic calculus for convoluted Lévy processes. Bernoulli 14 (2008), no. 2, 499--518. doi:10.3150/07-BEJ115.

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