Geodesic
Transformation of measure for diffusions with double-break drift
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 58-69 
A. N. Borodin. Transformation of measure for diffusions with double-break drift. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 58-69. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a4/
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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. It is essential that we have a double-break drift. It is possible for the drift 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.

[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, “Preobrazovanie mery dlya diffuzii s razryvnym snosom”, Zap. nauchn. semin. POMI, 515, 2022, 72–82

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

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