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DTSTART:20200308T070000
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DTSTART:20191103T060000
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DTSTART;TZID=America/Toronto:20200723T160000
SEQUENCE:0
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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:APPLICATIONS OF NONSTANDARD ANALYSIS TO MARKOV PROCESSES\n\n--
 -----------------------\n\nNonstandard analysis\, a powerful machinery der
 ived from mathematical\nlogic\, has had many applications in probability t
 heory as well as\nstochastic processes. Nonstandard analysis allows constr
 uction of a\nsingle object---a hyperfinite probability space---which satis
 fies all\nthe first order logical properties of a finite probability space
 \, but\nwhich can be simultaneously viewed as a measure-theoretical\nproba
 bility space via the Loeb construction. As a consequence\, the\nhyperfinit
 e/measure duality has proven to be particularly in porting\ndiscrete resul
 ts into their continuous settings. \n\nIn this talk\, for every general-s
 tate-space discrete-time Markov\nprocess satisfying appropriate conditions
 \, we construct a hyperfinite\nMarkov process which has all the basic orde
 r logical properties of a\nfinite Markov process to represent it.  We sho
 w that the mixing time\nand the hitting time agree with each other up to s
 ome multiplicative\nconstants for discrete-time general-state-space revers
 ible Markov\nprocesses satisfying certain condition. Finally\, we show tha
 t our\nresult is applicable to a large class of Gibbs samplers and\nMetrop
 olis-Hasting algorithms.\n\nPLEASE NOTE: This seminar will be delivered on
 line through Webex. To\njoin\, please follow this link: Virtual seminar by
  Kevin (Haosui)\nDuanmu.\n[https://uwaterloo.webex.com/uwaterloo/onstage/g
 .php?MTID=e11f70a9375d2a134e344a3d848cdd848]
DTSTAMP:20260406T213748Z
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