Girsanov theory under a finite entropy condition
Léonard, Christian
HAL, hal-00558067 / Harvested from HAL
Text on HAL
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).
Publié le : 2012-07-05
Classification:  Girsanov's theory,  relative entropy,  processes with jumps,  diffusion processes,  Stochastic processes,  60G07, 60J60, 60J75, 60G44,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00558067,
     author = {L\'eonard, Christian},
     title = {Girsanov theory under a finite entropy condition},
     journal = {HAL},
     volume = {2012},
     number = {0},
     year = {2012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00558067}
}

Léonard, Christian. Girsanov theory under a finite entropy condition. HAL, Tome 2012 (2012) no. 0, . http://gdmltest.u-ga.fr/item/hal-00558067/