Semimartingale obliquely reflecting diffusions in curved nonsmooth domains

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• Cristina Costantini (Università degli Studi di Chieti-Pescara)
• Wednesday 07 August 2024, 10:00-11:00
• External.

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SSDW02 - Stochastic reflection

In this talk I will show how a recent reverse ergodic theorem for inhomogeneous, killed Markov chains can be used to uniquely characterise a semimartingale obliquely reflecting diffusion in some nonsmooth domains. In particular I will discuss two significant cases. In a 2-dimensional piecewise C1 domain, one can prove uniqueness under optimal conditions on the directions of reflection. In fact, in the case of a convex polygon, our conditions reduce to the well known completely-S condition, which is necessary; thus they strictly improve the Dupuis and Ishii (1993) conditions. Moreover our conditions allow for cusps in the boundary of the domain. 2-dimensional piecewise  C1 domains are of interest, for instance, in some singular stochastic control problems. In a piecewise C2  cone in arbitrary dimension, one can prove uniqueness for directions of reflection that have radial limits at the vertex, assuming the existence of certain Lyapunov functions. Examples will be given where this condition is met. Piecewise smooth cones are of interest, for instance, in diffusion approximation of some stochastic networks. Time permitting, some existence results in arbitrary dimension will also be discussed. These are obtained bythe constrained martingale problem approach. This presentation is based on joint works with T.G. Kurtz and a preprint.

This talk is part of the Isaac Newton Institute Seminar Series series.

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