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2011

Girsanov theory under a finite entropy condition

Léonard, Christian

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Understand

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.

Girsanov theory under a finite entropy condition · Around

Built on

Multivariate point processes: predictable representation, Radon-Nikodým derivatives, representation of martingales
J. Jacod · 1975
Earlier work this paper cites.
Calcul stochastique et problèmes de martingales
J. Jacod · 1979
Earlier work this paper cites.

Similar

Limit theorems for stochastic processes
J. Jacod and A.N. Shiryaev · 1987
Cited alongside, same era.
Theory of Orlicz spaces
M.M. Rao and Z.D. Ren · 1991
Cited alongside, same era.

Then

Continuous martingales and Brownian motion
D. Revuz and M. Yor · 1999
Later among the works it cites.
Stochastic integration and differential equations
P. E. Protter · 2004
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