Product and Moment Formulas for Iterated Stochastic Integrals (associated with L\'evy Processes)

Paolo Di Tella; Christel Geiss

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arXiv · 1808.10670

Product and Moment Formulas for Iterated Stochastic Integrals (associated with L\'evy Processes)

Paolo Di Tella·Christel Geiss

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Abstract

In this paper, we obtain explicit product and moment formulas for products of iterated integrals generated by families of square integrable martingales associated with an arbitrary L\'evy process. We propose a new approach applying the theory of compensated-covariation stable families of martingales. Our main tool is a representation formula for products of elements of a compensated-covariation stable family, which enables to consider L\'evy processes, with both jumps and Gaussian part.

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Paolo Di Tella, Christel Geiss. 2018-08-31. Product and Moment Formulas for Iterated Stochastic Integrals (associated with L\'evy Processes). https://arxiv.org/abs/1808.10670

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