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Hyperfinite stochastic integration for Lévy processes with finite-variation jump part


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  • Frederik Herzberg

    (Institute of Mathematical Economics, Bielefeld University)


This article links the hyperfinite theory of stochastic integration with respect to certain hyperfinite Lévy processes with the elementary theory of pathwise stochastic integration with respect to pure-jump Lévy processes with finite-variation jump part. Since the hyperfinite Itô integral is also defined pathwise, these results show that hyperfinite stochastic integration provides a pathwise definition of the stochastic integral with respect to Lévy jump-diffusions with finite-variation jump part. As an application, we provide a short and direct nonstandard proof of the generalized Itô formula for stochastic differentials of smooth functions of Lévy jump-diffusions whose jumps are bounded from below in norm.

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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 404.

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Length: 21 pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:bie:wpaper:404

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Related research

Keywords: Lévy processes; stochastic integration; nonstandard analysis; Itô formula;

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