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SUMMARY:A Positive Recurrent Reflecting Brownian Motion with Divergent Flu
 id Path - Bramson\, M (Minnesota)
DTSTART:20100325T093000Z
DTEND:20100325T103000Z
UID:TALK23841@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Precise conditions are known for positive recurrence of semima
 rtingale reflecting Brownian motion (SRBM) in 2 and 3 dimensions\, with th
 e argument in 3 dimensions being more involved than in 2 dimensions. The s
 etting in 4 and more dimensions is more complicated than in 3 dimensions a
 nd there are presently no general results. Associated with each SRBM are f
 luid paths\, which are solutions of deterministic equations corresponding 
 to the random equations of the SRBM. A standard result of Dupuis and Willi
 ams states that when every fluid path associated with the SRBM is attracte
 d to the origin\, the SRBM is positive recurrent. This result was employed
  by El Kharroubi et al. to give sufficient conditions for positive recurre
 nce in 3 dimensions. In a recent paper with Dai and Harrison\, it was show
 n that the above fluid path behavior is also necessary for positive recurr
 ence of the SRBM. Here\, we present a family of examples in 6 dimensions w
 here the SRBM is positive recurrent but for which a linear fluid path dive
 rges to infinity. These examples show\, in particular\, that the converse 
 of the Dupuis-Williams result does not hold in 6 and more dimensions. They
  also illustrate the difficulty in formulating conditions for positive rec
 urrence of SRBM in higher dimensions. 
LOCATION:Seminar Room 1\, Newton Institute
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