Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates

Lorenzo Bertini; Raphael Chetrite; Alessandra Faggionato; Davide Gabrielli

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Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates

机译：级别2.5连续时间马尔可夫链的大偏差随时间定期速率

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摘要

We consider an irreducible continuous-time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for the empirical measure and current. By contraction, we get the large deviation principle of three types of entropy production flow. We derive some Gallavotti–Cohen duality relations and discuss some applications.

机译：我们考虑有限状态空间的不可缩短的连续时间马尔可夫链，随着时间的定期跳跃速率，并证明了经验测量和流量的关节大偏差原理，以及对经验测量和电流的联合大偏差原理。通过收缩，我们得到了三种类型的熵生产流程的大偏差原理。我们派生了一些Gallavotti-Cohen二元关系，并讨论了一些应用程序。

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《Annales Henri Poincare》 |2018年第10期|共42页
作者
Lorenzo Bertini; Raphael Chetrite; Alessandra Faggionato; Davide Gabrielli;
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作者单位

Dipartimento di Matematica Università di Roma ‘La Sapienza’;

CNRS Laboratoire J.A. Dieudonné Université C?te d’Azur;

Dipartimento di Matematica Università di Roma ‘La Sapienza’;

DISIM Università dell’Aquila;

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正文语种 eng
中图分类理论物理学;
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1. Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates [J] . Lorenzo Bertini, Raphael Chetrite, Alessandra Faggionato, Annales Henri Poincare . 2018,第10期

机译：级别2.5连续时间马尔可夫链的大偏差随时间定期速率
2. Moderate deviations for time-varying dynamic systems driven by non-homogeneous Markov chains with Two-time Scales [J] . Qi He, G. Yin Stochastics: An International Journal of Probability and Stochastic Processes . 2014,第1a3期

机译：由具有二阶标度的非齐次马尔可夫链驱动的时变动态系统的中度偏差
3. The deviation matrix of a continuous-time markov Chain [J] . Pauline Coolen-Schrijner, Erik A. van Doorn Probability in the Engineering and Informational Sciences . 2002,第3期

机译：连续时间马尔可夫链的偏差矩阵
4. Formal analysis and validation of continuous-time Markov chain based system level power management strategies [C] . Gethin Norman, David Parker, Marta Kwiatkowska, IEEE International High-Level Design Validation and Test Workshop . 2002

机译：基于连续时间马尔可夫链的系统级电力管理策略的正式分析与验证
5. Analysis of bivariate longitudinal discrete data: A joint continuous-time Markov chains approach [D] . Wu, Chih-Hsien 2016

机译：二元纵向离散数据分析：联合连续时间马尔可夫链方法
6. SIMULATION FROM ENDPOINT-CONDITIONED CONTINUOUS-TIME MARKOV CHAINS ON A FINITE STATE SPACE WITH APPLICATIONS TO MOLECULAR EVOLUTION [O] . Asger Hobolth, Eric A. Stone -1

机译：动态模拟端点空调连续时间的马尔可夫链在有限状态空间应用程序分子进化
7. Level 2.5 large deviations for continuous time Markov chains with time periodic rates [O] . Bertini, L., Chetrite, R., Faggionato, A., 2017

机译：连续时间markov链随时间的2.5级大偏差定期费率
8. Deviation Matrix of a Continuous-Time Markov Chain. [R] . Coolen-Schrijner, P., Van Doorn, E. A. 2001

机译：连续时间马尔可夫链的偏差矩阵。

Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates

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