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

Pierre Étoré and Miguel Martinez

Stochastic Processes and their Applications, 2018, vol. 128, issue 8, 2642-2687

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 SDEs under mild assumptions, we explore their link with Parabolic Differential Equations (PDE) with transmission conditions. We study the regularity of solutions of such PDEs and ensure the validity of a Feynman–Kac representation formula. These results are then used to characterize the solutions of these SDEs as time inhomogeneous Markov Feller processes.

Keywords: Stochastic Differential Equations with Local Time; Time inhomogeneous Skew Brownian Motion; Divergence Form Operators; Feynman–Kac representation formula; Time inhomogeneous Markov processes (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:8:p:2642-2687

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DOI: 10.1016/j.spa.2017.09.018

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