BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A Positive Recurrent Reflecting Brownian Motion wi
th Divergent Fluid Path - Bramson\, M (Minnesota)
DTSTART;TZID=Europe/London:20100325T093000
DTEND;TZID=Europe/London:20100325T103000
UID:TALK23841AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23841
DESCRIPTION:Precise conditions are known for positive recurren
ce of semimartingale reflecting Brownian motion (S
RBM) in 2 and 3 dimensions\, with the argument in
3 dimensions being more involved than in 2 dimensi
ons. The setting in 4 and more dimensions is more
complicated than in 3 dimensions and there are pre
sently no general results. Associated with each SR
BM are fluid paths\, which are solutions of determ
inistic equations corresponding to the random equa
tions of the SRBM. A standard result of Dupuis and
Williams states that when every fluid path associ
ated with the SRBM is attracted to the origin\, th
e SRBM is positive recurrent. This result was empl
oyed by El Kharroubi et al. to give sufficient con
ditions for positive recurrence in 3 dimensions. I
n a recent paper with Dai and Harrison\, it was sh
own that the above fluid path behavior is also nec
essary for positive recurrence 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 diverges to infinity. These ex
amples show\, in particular\, that the converse of
the Dupuis-Williams result does not hold in 6 and
more dimensions. They also illustrate the difficu
lty in formulating conditions for positive recurre
nce of SRBM in higher dimensions.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
END:VEVENT
END:VCALENDAR