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SUMMARY:Claudio del Sole (Università bocconi di Milano)
DTSTART:20211028T150000Z
DTEND:20211028T153000Z
DTSTAMP:20260421T124157Z
UID:MoRN/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoRN/38/">Sc
 aling limits of stochastic models with Fast Absorption and Slow Escape</a>
 \nby Claudio del Sole (Università bocconi di Milano) as part of Seminar o
 n the Mathematics of Reaction Networks\n\n\nAbstract\nAutocatalytic reacti
 on systems often exhibit a peculiar switching behaviour\, due to random fl
 uctuations and discreteness in the number of molecules\, which produces th
 e phenomenon of discreteness-induced transitions. The 2-dimensional versio
 n of a model proposed by Togashi and Kaneko (2001) is a prominent example 
 of such patten. We analyze this model within a multiscale framework\, in w
 hich fast autocatalytic cascades are triggered by much slower inflow and o
 utflow reactions. Under suitable assumptions\, we study the limit behaviou
 r of the rescaled stochastic process\, and prove weak convergence to a nat
 urally arising piecewise-deterministic Markov process on the Skorohod spac
 e equipped with Jakubowsky S-topology. Building upon this model\, we discu
 ss extensions of such procedure to a larger family of autocatalytic reacti
 on systems\, in which a fast subsystem is rapidly absorbed into a set of a
 bsorbing states\, occasionally giving rise to abrupt state switches of pos
 sibly random size.\n
LOCATION:https://researchseminars.org/talk/MoRN/38/
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