Large deviations of the empirical flow for continuous time Markov chains

By Lorenzo Bertini, A. Faggionato, D. Gabrielli. 2012

83 citations recorded by the source corpus.

We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contraction from the empirical process.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2a483656701d6d515790d9d2b9278c8716223c99

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. R. Chetrite
2. Hugo Touchette

In Statistical and Nonlinear Physics

1. Hugo Touchette
2. R. Chetrite
3. U. Seifert
4. James H. Luscombe
5. Bérengère Dubrulle
6. Juan P. Garrahan
7. P. Hänggi
8. Valerio Lucarini

In Statistics and Probability

1. Hugo Touchette
2. R. Chetrite

Citations in the corpus

• Dissipation Bounds All Steady-State Current Fluctuations. (2015, unknown): “apðy; zÞ≡ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pðyÞpðzÞrðy; zÞrðz; yÞ p , and jpðy; zÞ≡ pðyÞrðy; zÞ − pðzÞrðz; yÞ is the mean current associated with the empirical density [29,36,37].”
• Nonequilibrium Markov Processes Conditioned on Large Deviations (2014, background): “This level has been studied formally in [90,95,96], and rigorously for jump processes with finite space in [100] and countable space in [101].”