Localization for constrained martingale problems and optimal conditions for uniqueness of reflecting diffusions in 2-dimensional domains

Cristina Costantini and Thomas G. Kurtz

Stochastic Processes and their Applications, 2024, vol. 170, issue C

Abstract: We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each “side”, under geometric, easily verifiable conditions. Our conditions are optimal in the sense that, in the case of a convex polygon, they reduce to the conditions of Dai and Williams (1996), which are necessary for existence of reflecting Brownian motion. Moreover our conditions allow for cusps.

Keywords: Reflecting diffusion; Oblique reflection; Nonsmooth domain; Cusp; Constrained martingale problem; Jump boundary conditions (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104295

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