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SUMMARY:Stochastic Simulation with Piecewise-Deterministic Markov Processe
 s - Sam Power (University of Cambridge)
DTSTART:20190529T150000Z
DTEND:20190529T160000Z
UID:TALK125737@talks.cam.ac.uk
CONTACT:59181
DESCRIPTION:To draw approximate samples from a distribution p on a continu
 ous state-space\, a time-honoured approach is to simulate a Markov process
  X_t with p as its invariant measure. Historically\, this has been achieve
 d by use of stochastic differential equations (SDEs)\, but in recent years
 \, there has been an increasing amount of attention paid to Piecewise-Dete
 rministic Markov Processes (PDMPs). These are an alternative class of Mark
 ov processes which use a combination of deterministic dynamics and discret
 e jumps to suppress random-walk behaviour and reach equilibrium rapidly.\n
 \nAlthough the PDMP framework accommodates a wide range of underlying dyna
 mics in principle\, existing approaches have tended to use quite simple dy
 namics\, such as straight lines and elliptical orbits. In this work\, I pr
 esent a procedure which elucidates how one can use a general dynamical sys
 tem in the PDMP framework to sample from a given measure. The procedure ma
 kes use of `trajectorial reversibility’\, a generalisation of `detailed 
 balance’ which allows for tractable computation with otherwise non-rever
 sible processes. Correctness of the procedure is established in a general 
 setting\, and specific\, constructive recommendations are made for how to 
 implement the resulting algorithms in practice.\n\nNo background in stocha
 stic simulation will be assumed\, and emphasis will be placed on outlining
  and understanding the key mechanisms which dictate the behaviour of PDMPs
 .
LOCATION:MR14\, Centre for Mathematical Sciences
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