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SUMMARY:Semimartingale obliquely reflecting diffusions in curved nonsmooth
  domains - Cristina Costantini (Università degli Studi di Chieti-Pescara)
DTSTART:20240807T090000Z
DTEND:20240807T100000Z
UID:TALK215671@talks.cam.ac.uk
DESCRIPTION:In this talk I will show how a recent reverse ergodic theorem 
 for inhomogeneous\, killed Markov chains can be used to uniquely character
 ise a semimartingale obliquely reflecting diffusion in some nonsmooth doma
 ins.\nIn particular I will discuss two significant cases. In a 2-dimension
 al piecewise&nbsp\;C1 domain\, one can prove uniqueness under optimal cond
 itions 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 (199
 3) conditions. Moreover our conditions allow for cusps in the boundary of 
 the domain. 2-dimensional piecewise &nbsp\;C1 domains are of interest\, fo
 r instance\, in some singular stochastic control problems.\nIn a piecewise
  C2&nbsp\; cone in arbitrary dimension\, with no cusplike singularities\, 
 one can prove uniqueness assuming&nbsp\; conditions analogous to the 2-dim
 ensional case and the existence of certain Lyapunov functions. Piecewise s
 mooth cones are of interest\, for instance\, in diffusion approximation of
  some stochastic networks. I will give an example from diffusion approxima
 tion of stochastic networks where all the above conditions are met.&nbsp\;
 \nTime permitting\, some existence results in arbitrary dimension will als
 o be discussed. These are obtained by the constrained martingale problem a
 pproach.&nbsp\;\nThis presentation is based on joint works with T.G. Kurtz
  and a preprint.
LOCATION:External
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