Nous montrons que toute chaîne de Markov sans cycles sur un espace discret peut être vue comme un processus ponctuel determinantal. Comme application, nous démontrons des théorèmes limites centrales pour le nombre de particules dans une fenêtre pour des processus de renouvellement et des processus de renouvellement markoviens avec un bruit de Bernoulli.
We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.
Mots clés : Markov chain, determinantal point process
@article{AIHPB_2008__44_1_19_0, author = {Borodin, Alexei}, title = {Loop-free {Markov} chains as determinantal point processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {19--28}, publisher = {Gauthier-Villars}, volume = {44}, number = {1}, year = {2008}, doi = {10.1214/07-AIHP115}, mrnumber = {2451569}, language = {en}, url = {http://www.numdam.org/articles/10.1214/07-AIHP115/} }
TY - JOUR AU - Borodin, Alexei TI - Loop-free Markov chains as determinantal point processes JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2008 SP - 19 EP - 28 VL - 44 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/07-AIHP115/ DO - 10.1214/07-AIHP115 LA - en ID - AIHPB_2008__44_1_19_0 ER -
%0 Journal Article %A Borodin, Alexei %T Loop-free Markov chains as determinantal point processes %J Annales de l'I.H.P. Probabilités et statistiques %D 2008 %P 19-28 %V 44 %N 1 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/07-AIHP115/ %R 10.1214/07-AIHP115 %G en %F AIHPB_2008__44_1_19_0
Borodin, Alexei. Loop-free Markov chains as determinantal point processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 1, pp. 19-28. doi : 10.1214/07-AIHP115. http://www.numdam.org/articles/10.1214/07-AIHP115/
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