کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1155430 958726 2015 34 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Flows, currents, and cycles for Markov chains: Large deviation asymptotics
ترجمه فارسی عنوان
جریان، جریان و چرخه برای زنجیره مارکوف: تقارن بزرگ انحراف
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

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 L1L1 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 125, Issue 7, July 2015, Pages 2786–2819
نویسندگان
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