Hyperfinite stochastic integration for Lévy processes with finite-variation jump part |
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Authors: | Frederik S. Herzberg |
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Affiliation: | a Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA b Institut für Mathematische Wirtschaftsforschung, Universität Bielefeld, Universitätsstraße 25, D-33615 Bielefeld, Germany |
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Abstract: | 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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Keywords: | primary, 03H05, 28E05, 60G51 secondary, 60H05 |
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