Parametrix Methods for One-Dimensional Reflected SDEs

Aurélien Alfonsi (1, 2) , Masafumi Hayashi (3) , Arturo Kohatsu-Higa (4)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHRISK - Mathematical Risk Handling
3 University of the Ryukyus [Okinawa]
4 Department of Mathematical Sciences, Ritsumeikan Universtiy

In this article, we revisit in a didactic manner the forward and backward approaches of the parametrix method for one-dimensional reflected stochastic differential equations on the half line. We give probabilistic expressions for the expectation of functionals of its solution and we also discuss properties of the associated density.

Mots clés: Parametrix method; Reflected SDEs; Probabilistic representation

Domaines: Probabilités [math.PR]

Aurélien Alfonsi, Masafumi Hayashi, Arturo Kohatsu-Higa. Parametrix Methods for One-Dimensional Reflected SDEs. Modern Problems of Stochastic Analysis and Statistics Selected Contributions In Honor of Valentin Konakov , Springer Proceedings in Mathematics & Statistics (208), Springer, 2017, 978-3-319-65313-6. ⟨10.1007/978-3-319-65313-6_3⟩. ⟨hal-01670011⟩