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SUMMARY:Stochastic networks and semimartingale reflecting Brownian motions
  in piecewise smooth domains - Ruth Williams\, Department of Mathematics\,
  University of California\, San Diego
DTSTART:20070713T130000Z
DTEND:20070713T140000Z
UID:TALK7635@talks.cam.ac.uk
CONTACT:6123
DESCRIPTION:Semimartingale Reflecting Brownian Motions (SRBMs) living in t
 he closures\nof domains with piecewise smooth boundaries are of interest i
 n applied\nprobability because of their role as heavy traffic approximatio
 ns for\nstochastic networks. Modern applications such as bandwidth\nsharin
 g and packet switches can yield stochastic network models and\nSRBM approx
 imations that are more general than those associated\nwith conventional mu
 lticlass queueing networks.\nIn justifying the approximation of a stochast
 ic network by an SRBM\, a\ncrucial step is the use of a perturbation resul
 t or invariance principle.\nIn essence this implies that a process\nsatisf
 ying the definition of an SRBM\, except for small random\nperturbations in
  the defining conditions\, is close in\ndistribution to an SRBM.\nHere we 
 describe sufficient conditions for an invariance principle to\nhold for SR
 BMs in piecewise smooth domains.\nA crucial ingredient in the proof of thi
 s\nresult is an oscillation inequality for solutions of a perturbed\nSkoro
 khod problem.\nSome applications of our results and open problems will be 
 discussed.\n\n
LOCATION: Centre for Mathematical Sciences\, Room 12
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