PUB - Publikationen an der Universität Bielefeld

This article links the hyperfinite theory of stochastic integration with respect to certain hyperfinite Levy processes with the elementary theory of pathwise stochastic integration with respect to pure-jump Levy processes with finite-variation jump part. Since the hyperfinite Ito integral is also defined pathwise, these results show that hyperfinite stochastic integration provides a pathwise definition of the stochastic integral with respect to Levy jump-diffusions with finite-variation jump part. As an application, we provide a short and direct nonstandard proof of the generalized Ito formula for stochastic differentials of smooth functions of Levy jump-diffusions whose jumps are bounded from below in norm. (C) 2010 Elsevier Masson SAS. All rights reserved.