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DTSTART;TZID=America/Toronto:20200723T160000
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URL:/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:20250517T231644Z
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