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DTSTAMP:20261030T222545Z
SUMMARY:Dynamical Systems Seminar – Tresnia Berah (Imperial)
DESCRIPTION:Speaker: Tresnia Berah\nTitle: Selection principles for quasi-s
 tationary distributions and reinforcement processes\nAbstract: (https://a
 rxiv.org/abs/2606.25857) Let P be a sub-Markov matrix on a finite set S. W
 e study a reinforced process that evolves according to P until absorption 
 and is then resurrected at a point sampled from its weighted past occupati
 on measure ??\, with positive weights w? and cumulative weights W? = w? + 
 ? + w?. Whereas the irreducible case leads to almost sure convergence towa
 rds the unique quasi-stationary distribution (QSD)\, we consider reducible
  kernels\, for which several QSDs may coexist. Under generic assumptions o
 n P and suitable assumptions on the weights and initial condition\, there 
 are finitely many QSDs and the asymptotic selection is governed by the sum
 mability of 1/W?. If the series ? 1/W? diverges\, then ?? converges almost
  surely towards the QSD associated with the largest Perron value. If the s
 eries converges\, then ?? converges almost surely towards a QSD\, and each
  QSD is selected with positive probability. For polynomial weights w? = 1 
 and w? = k^q for k ? 1\, the first regime corresponds to ?1 ? q ? 0 and th
 e second to q > 0.
URL:https://www.imperial.ac.uk/events/215884/dynamical-systems-seminar-tres
 nia-berah-imperial/
DTSTART;TZID=Europe/London:20261103T130000
DTEND;TZID=Europe/London:20261103T140000
LOCATION:145\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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