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SUMMARY:Stationary random walks with a switch - Vladislav Vysotskiy (Unive
 rsity of Sussex)
DTSTART:20240814T140000Z
DTEND:20240814T150000Z
UID:TALK219397@talks.cam.ac.uk
DESCRIPTION:A switching random walk\, commonly known under the misnomer `o
 scillating random walk'\, is a real-valued Markov chain whose distribution
  of increments depends only on the sign of the current position. Such chai
 ns are closely related to reflected random walks on the positive half-line
 .\nWe find an invariant measure for a switching random walk and prove its 
 uniqueness within the class of locally finite measures in a number of case
 s\, including where the switching walk is recurrent. In the particular cas
 e where the switching walk is an actual random walk\, our proof establishe
 s a natural relationship between stationarity of the walk relative to the 
 Lebesgue measure and stationarity of the renewal processes of its ascendin
 g and descending ladder heights\, a classical result of the renewal theory
 .\n&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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