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MALLIAVIN CALCULUS AND ANTICIPATIVE ITÔ FORMULAE FOR LÉVY PROCESSES

Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway

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THILO MEYER-BRANDIS

Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway

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BERNT ØKSENDAL

Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway

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, and

FRANK PROSKE

Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, P. O. Box 1053 Blindern, N-0316 Oslo, Norway

Also at Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway.

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https://doi.org/10.1142/S0219025705001950Cited by:42 (Source: Crossref)

Abstract

We introduce the forward integral with respect to a pure jump Lévy process and prove an Itô formula for this integral. Then we use Mallivin calculus to establish a relationship between the forward integral and the Skorohod integral and apply this to obtain an Itô formula for the Skorohod integral.

Keywords:

AMSC: 60H40, 60G51, 60G57, 60H07

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