On considère une chaîne de Markov en temps continu à espace d’états denombrable, et on prouve un principe de grandes déviations commun pour la mesure empirique et le courant empirique, qui représente le nombre total de sauts entre les paires d’états. On donne une preuve directe à l’aide d’un tilting, et une preuve indirecte par contraction, à partir du processus empirique.
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.
@article{AIHPB_2015__51_3_867_0, author = {Bertini, Lorenzo and Faggionato, Alessandra and Gabrielli, Davide}, title = {Large deviations of the empirical flow for continuous time {Markov} chains}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {867--900}, publisher = {Gauthier-Villars}, volume = {51}, number = {3}, year = {2015}, doi = {10.1214/14-AIHP601}, mrnumber = {3365965}, zbl = {1323.60045}, language = {en}, url = {http://www.numdam.org/articles/10.1214/14-AIHP601/} }
TY - JOUR AU - Bertini, Lorenzo AU - Faggionato, Alessandra AU - Gabrielli, Davide TI - Large deviations of the empirical flow for continuous time Markov chains JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2015 SP - 867 EP - 900 VL - 51 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/14-AIHP601/ DO - 10.1214/14-AIHP601 LA - en ID - AIHPB_2015__51_3_867_0 ER -
%0 Journal Article %A Bertini, Lorenzo %A Faggionato, Alessandra %A Gabrielli, Davide %T Large deviations of the empirical flow for continuous time Markov chains %J Annales de l'I.H.P. Probabilités et statistiques %D 2015 %P 867-900 %V 51 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/14-AIHP601/ %R 10.1214/14-AIHP601 %G en %F AIHPB_2015__51_3_867_0
Bertini, Lorenzo; Faggionato, Alessandra; Gabrielli, Davide. Large deviations of the empirical flow for continuous time Markov chains. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 867-900. doi : 10.1214/14-AIHP601. http://www.numdam.org/articles/10.1214/14-AIHP601/
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