 Flows, currents, and cycles for Markov chains: Large deviation asymptoticsLorenzo Bertini, Alessandra Faggionato and Davide Gabrielli Stochastic Processes and their Applications, 2015, vol. 125, issue 7, 2786-2819 Abstract: We consider a continuous time Markov chain on a countable state space. We prove a joint large deviation principle (LDP) of the empirical measure and current in the limit of large time interval. The proof is based on results on the joint large deviations of the empirical measure and flow obtained in Bertini et al. (in press). By improving such results we also show, under additional assumptions, that the LDP holds with the strong L1 topology on the space of currents. We deduce a general version of the Gallavotti–Cohen (GC) symmetry for the current field and show that it implies the so-called fluctuation theorem for the GC functional. We also analyze the large deviation properties of generalized empirical currents associated to a fundamental basis in the cycle space, which, as we show, are given by the first class homological coefficients in the graph underlying the Markov chain. Finally, we discuss in detail some examples. Keywords: Markov chain; Large deviations; Empirical flow; Empirical current; Cellular homology; Gallavotti–Cohen fluctuation theorem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:7:p:2786-2819 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2015.02.001 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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