Geodesic
Transformation of measure for diffusions with discontinuous drift
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 72-82 
A. N. Borodin. Transformation of measure for diffusions with discontinuous drift. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 72-82. http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a4/
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     title = {Transformation of measure for diffusions with discontinuous drift},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider transformation of measure for diffusions with discontinuous drift analogous to the Girsanov transformation. For the drift it is possible to extract discontinuous component as a step function and derive the transformation of the measure of initial diffusion to the measure of diffusion with continuous drift. It is considered an application of the general result to the Ornstein–Uhlenbeck process with discontinuous drift.

[1] I. V. Girsanov, “O preobrazovanii odnogo klassa sluchainykh protsessov s pomoschyu absolyutno nepreryvnoi zameny mery”, Teoriya veroyatn. i ee primen., 5:2 (1960), 314–330 | MR

[2] A. N. Borodin, Sluchainye protsessy, Lan, Sankt-Peterburg, 2013

[3] A. N. Borodin, “Raspredeleniya funktsionalov ot skoshennogo brounovskogo dvizheniya s razryvnym snosom”, Zap. nauchn. semin. POMI, 501, 2021, 36–51

[4] A. N. Borodin, P. Salminen, Spravochnik po brounovskomu dvizheniyu. Fakty i formuly, Lan, Sankt-Peterburg, 2016