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DTSTART:20200308T070000
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DTSTART:20191103T060000
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DTSTART;TZID=America/Toronto:20200723T160000
SEQUENCE:0
TRANSP:TRANSPARENT
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URL:https://uwaterloo.ca/statistics-and-actuarial-science/events/department
-seminar-kevin-haosui-duanmu-uc-berkeley
SUMMARY:Department Seminar by Kevin (Haosui) Duanmu\, UC Berkeley
CLASS:PUBLIC
DESCRIPTION:Summary \n\nAPPLICATIONS OF NONSTANDARD ANALYSIS TO MARKOV PRO
CESSES\n\n-------------------------\n\nNonstandard analysis\, a powerful m
achinery derived from mathematical\nlogic\, has had many applications in p
robability theory as well as\nstochastic processes. Nonstandard analysis a
llows construction of a\nsingle object---a hyperfinite probability space--
-which satisfies all\nthe first order logical properties of a finite proba
bility space\, but\nwhich can be simultaneously viewed as a measure-theore
tical\nprobability space via the Loeb construction. As a consequence\, the
\nhyperfinite/measure duality has proven to be particularly in porting\ndi
screte results into their continuous settings. \n\nIn this talk\, for eve
ry general-state-space discrete-time Markov\nprocess satisfying appropriat
e conditions\, we construct a hyperfinite\nMarkov process which has all th
e basic order logical properties of a\nfinite Markov process to represent
it. We show that the mixing time\nand the hitting time agree with each o
ther up to some multiplicative\nconstants for discrete-time general-state-
space reversible Markov\nprocesses satisfying certain condition. Finally\,
we show that our\nresult is applicable to a large class of Gibbs samplers
and\nMetropolis-Hasting algorithms.\n\nPLEASE NOTE: This seminar will be
delivered online through Webex. To\njoin\, please follow this link: Virtua
l seminar by Kevin (Haosui)\nDuanmu.\n[https://uwaterloo.webex.com/uwaterl
oo/onstage/g.php?MTID=e11f70a9375d2a134e344a3d848cdd848]\n
DTSTAMP:20240304T140237Z
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