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SUMMARY:Positive Markov processes in Laplace duality
DTSTART:20251218T130000Z
DTEND:20251218T140000Z
DTSTAMP:20260504T051500Z
UID:indico-event-14636@indico.math.cnrs.fr
DESCRIPTION:Speakers: Clément Foucart\n\nThe purpose of this talk\, based
  on joint work with Matija Vidmar\, is to investigate the class of positiv
 e Markov processes that admit a Laplace duality relationship: the Laplace 
 transforms of the processes are related through an exchange of the argumen
 t and the initial state. This type of duality naturally emerges for instan
 ce in systems with branching phenomena. Beyond the classical branching fra
 mework\, we show that a wide variety of processes and generators fall with
 in the scope of Laplace duality.\nFirst\, from a theoretical perspective\,
  we establish that a process admits a Laplace dual if and only if its semi
 group leaves invariant the space of completely monotone functions (subject
  to conventions for 0 × ∞ and ∞ × 0). In a more constructive directi
 on\, we then identify seven fundamental building blocks from which such du
 ality can be constructed. The associated processes can be viewed as genera
 lisations of continuous-state branching processes and include several mode
 ls — sometimes discovered independently of the duality perspective — u
 sed to represent random environments\, immigration\, collisions\, and othe
 r dynamics. A key analytical tool\, developed here in a general and unifyi
 ng setting\, is the notion of a Laplace symbol associated with a generator
 .\n\nhttps://indico.math.cnrs.fr/event/14636/
LOCATION:435 (ENS)
URL:https://indico.math.cnrs.fr/event/14636/
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