The Girsanov theorem without (so much) stochastic analysis - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Book Sections Year : 2018

The Girsanov theorem without (so much) stochastic analysis


In this pedagogical note, we construct the semi-group associated to a stochastic differential equation with a constant diffusion and a Lipschitz drift by composing over small times the semi-groups generated respectively by the Brownian motion and the drift part. Similarly to the interpretation of the Feynman-Kac formula through the Trotter-Kato-Lie formula in which the exponential term appears naturally, we construct by doing so an approximation of the exponential weight of the Girsanov theorem. As this approach only relies on the basic properties of the Gaussian distribution, it provides an alternative explanation of the form of the Girsanov weights without referring to a change of measure nor on stochastic calculus.
Fichier principal
Vignette du fichier
girsanov_FV_R1.pdf (532.1 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01498129 , version 1 (29-03-2017)
hal-01498129 , version 2 (06-10-2017)
hal-01498129 , version 3 (22-09-2018)



Antoine Lejay. The Girsanov theorem without (so much) stochastic analysis. Donati-Martin, Catherine; Lejay, Antoine; Rouault, Alain. Séminaire de Probabilités XLIX, 2215, Springer-Nature, 2018, 978-3-319-92419-9. ⟨10.1007/978-3-319-92420-5_8⟩. ⟨hal-01498129v3⟩
688 View
7549 Download



Gmail Facebook Twitter LinkedIn More