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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Semimartingale obliquely reflecting diffusions in curved nonsmooth domains

## Semimartingale obliquely reflecting diffusions in curved nonsmooth domainsAdd to your list(s) Download to your calendar using vCal - Cristina Costantini (Università degli Studi di Chieti-Pescara)
- Wednesday 07 August 2024, 10:00-11:00
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If you have a question about this talk, please contact nobody. 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, with no cusplike singularities, one can prove uniqueness assuming conditions analogous to the 2-dimensional case and the existence of certain Lyapunov functions. Piecewise smooth cones are of interest, for instance, in diffusion approximation of some stochastic networks. I will give an example from diffusion approximation of stochastic networks where all the above conditions are met. Time permitting, some existence results in arbitrary dimension will also be discussed. These are obtained by the 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. ## This talk is included in these lists:- All CMS events
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