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- W1512937803 abstract "We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, s)in Otimes G$, $O$ being a region in $bbR^d$ or the $d$--dimensional torus, $G$ being a finite set. The continuous variable $x$ follows a piecewise deterministic dynamics, the discrete variable $s$ evolves by a stochastic jump dynamics and the two resulting evolutions are fully--coupled. We study stationarity, reversibility and time--reversal symmetries of the process. Increasing the frequency of the $s$--jumps, we show that the system behaves asymptotically as deterministic and we investigate the structure of fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. cite{BDGJL1, BDGJL2, BDGJL3, BDGJL4}, in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti--Cohen--type symmetry relation with involution map different from time--reversal. For several examples the above results are recovered by explicit computations." @default.
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- W1512937803 date "2009-02-24" @default.
- W1512937803 modified "2023-09-27" @default.
- W1512937803 title "Stationarity, time--reversal and fluctuation theory for a class of piecewise deterministic Markov processes" @default.
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