Stationary distributions for jump processes with memory
Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 3, p. 609-630

We analyze a jump processes Z with a jump measure determined by a “memory” process S. The state space of (Z,S) is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of (Z,S) is the product of the uniform probability measure and a Gaussian distribution.

Nous proposons d’étudier un processus à sauts Z avec une mesure de sauts déterminée par un processus S représentant une “mémoire”. L’espace d’états de (Z,S) est le produit Cartesien du cercle trigonométrique et de l’axe réel. Nous démontrons que la distribution stationnaire de (Z,S) est la mesure produit d’une loi uniforme et d’une loi Gaussienne.

DOI : https://doi.org/10.1214/11-AIHP428
Classification:  60J35,  60H10,  60G51,  60J75,  60J55
Keywords: stationary distribution, stable Lévy process, process with memory
@article{AIHPB_2012__48_3_609_0,
     author = {Burdzy, K. and Kulczycki, T. and Schilling, R. L.},
     title = {Stationary distributions for jump processes with memory},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {3},
     year = {2012},
     pages = {609-630},
     doi = {10.1214/11-AIHP428},
     zbl = {1263.60072},
     mrnumber = {2976556},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2012__48_3_609_0}
}
Burdzy, K.; Kulczycki, T.; Schilling, R. L. Stationary distributions for jump processes with memory. Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 3, pp. 609-630. doi : 10.1214/11-AIHP428. http://www.numdam.org/item/AIHPB_2012__48_3_609_0/

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