Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators - Archive ouverte HAL Access content directly
Journal Articles Stochastic Processes and their Applications Year : 2018

Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators

Abstract

In this paper we study time-inhomogeneous versions of one-dimensional Stochastic Differential Equations (SDE) involving the Local Time of the unknown process on curves. After proving existence and uniqueness for these SDE under mild assumptions, we explore their link with Parabolic Differential Equations (PDE) with transmission conditions. We study the regularity of solutions of such PDE and ensure the validity of a Feynman-Kac representation formula. These results are then used to characterize the solutions of these SDE as time-inhomogeneous Markov Feller processes.
Fichier principal
Vignette du fichier
EDSTLinho_18092017.pdf (502.55 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01356270 , version 1 (25-08-2016)
hal-01356270 , version 2 (19-09-2017)

Identifiers

Cite

Pierre Etoré, Miguel Martinez. Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators. Stochastic Processes and their Applications, 2018, 128 (8), pp.2642-2687. ⟨10.1016/j.spa.2017.09.018⟩. ⟨hal-01356270v2⟩
438 View
1093 Download

Altmetric

Share

Gmail Facebook X LinkedIn More