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SUMMARY:Non-local birth-death processes - Giacomo Ascione (Università deg
 li Studi di Napoli Federico II)
DTSTART:20220223T090000Z
DTEND:20220223T093000Z
UID:TALK167759@talks.cam.ac.uk
DESCRIPTION:In this talk\, we introduce a class of time-non-local birth-de
 ath processes by applying a time-change\, via an independent inverse subor
 dinator\, to a class of solvable (classical) birth-death processes. Precis
 ely\, we consider a class of birth-death processes with polynomial birth a
 nd death rate and whose stationary distribution solves a discrete Pearson 
 equation. In particular\, the generator of the parent birth-death processe
 s can be seen as lattice approximations of the generators of the Pearson d
 iffusions. We use a spectral decomposition method to show existence and un
 iqueness of strong solutions of some time-non-local heat-like Cauchy probl
 ems on a sequence space induced by the generator of the birth-death proces
 ses and its adjoint operator. The non-local birth-death processes introduc
 ed before are then used to exploit a stochastic representation result for 
 such solutions. Finally\, some properties of these processes\, such as sta
 tionarity and long/short-range dependence\, are investigated. This talk is
  based on a joint work with Nikolai Leonenko (Cardiff University) and Enri
 ca Pirozzi (Universit&Atilde\; &nbsp\;degli Studi di Napoli).
LOCATION:Seminar Room 1\, Newton Institute
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