Stationarity, time--reversal and fluctuation theory for a class of piecewise deterministic Markov processes
| dc.creator | Faggionato, Alessandra | |
| dc.creator | Gabrielli, Davide | |
| dc.creator | Crivellari, Marco Ribezzi | |
| dc.date | 2009-02-24 | |
| dc.date.accessioned | 2026-07-07T12:46:16Z | |
| dc.date.available | 2026-07-07T12:46:16Z | |
| dc.description | We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in Ø\times \G$, $Ø$ 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. | |
| dc.description | 45 pages | |
| dc.identifier | https://arxiv.org/abs/0902.4195 | |
| dc.identifier | http://arxiv.org/abs/0902.4195 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221323 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.title | Stationarity, time--reversal and fluctuation theory for a class of piecewise deterministic Markov processes | |
| dc.type | text |