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Article Dans Une Revue Séminaire de probabilités de Strasbourg Année : 2012

Girsanov theory under a finite entropy condition

Christian Léonard
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Résumé

This paper is about Girsanov's theory. It (almost) doesn't contain new results but it is based on a simplified new approach which takes advantage of the (weak) extra requirement that some relative entropy is finite. Under this assumption, we present and prove all the standard results pertaining to the absolute continuity of two continuous-time processes with or without jumps. We have tried to give as much as possible a self-contained presentation. The main advantage of the finite entropy strategy is that it allows us to replace martingale representation results by the simpler Riesz representations of the dual of a Hilbert space (in the continuous case) or of an Orlicz function space (in the jump case).
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Dates et versions

hal-00558067 , version 1 (20-01-2011)
hal-00558067 , version 2 (31-01-2011)

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Citer

Christian Léonard. Girsanov theory under a finite entropy condition. Séminaire de probabilités de Strasbourg, 2012, Séminaire de probabilités de Strasbourg, 44, Lecture Notes in Mathematics (2046), pp.429-465. ⟨hal-00558067v2⟩
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