Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2021

Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps

Résumé

For one-dimensional jump-drift and jump-diffusion processes converging toward some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical time-averaged density, of the empirical time-averaged current and of the empirical time-averaged jump-flow are studied via the large deviations at level 2.5. Secondly, the joint probability of the empirical jumps and of the empirical excursions between consecutive jumps are analyzed via the large deviations at level 2.5 for the alternate Markov chain that governs the series of all the jump events of a long trajectory. These two general frameworks are then applied to three examples of positive jump-drift processes without diffusion, and to two examples of jump-diffusion processes, in order to illustrate various simplifications that may occur in rate functions and in contraction procedures.
Fichier principal
Vignette du fichier
2104.10392.pdf (385.08 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-03367009 , version 1 (11-01-2024)

Identifiants

Citer

Cecile Monthus. Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps. Journal of Statistical Mechanics: Theory and Experiment, 2021, 2021 (8), pp.083205. ⟨10.1088/1742-5468/ac12c5⟩. ⟨hal-03367009⟩
16 Consultations
9 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More