Conservation property of symmetric jump processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 3, p. 650-662

Motivated by the recent development in the theory of jump processes, we investigate its conservation property. We will show that a jump process is conservative under certain conditions for the volume-growth of the underlying space and the jump rate of the process. We will also present examples of jump processes which satisfy these conditions.

Motivés par les récents développements dans la théorie des processus de sauts, nous étudions leur propriété de conservation. Nous montrons qu'un processus de saut est conservatif sous certaines conditions sur la croissance du volume de l'espace sous-tendant et sur le taux de saut du processus. Nous donnons des exemples de processus satisfaisant ces conditions.

DOI : https://doi.org/10.1214/09-AIHP368
Classification:  60J75,  31C25,  35R09
Keywords: conservation property, symmetric Dirichlet forms with jumps, derivation property
@article{AIHPB_2011__47_3_650_0,
     author = {Masamune, Jun and Uemura, Toshihiro},
     title = {Conservation property of symmetric jump processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {3},
     year = {2011},
     pages = {650-662},
     doi = {10.1214/09-AIHP368},
     zbl = {1230.60090},
     mrnumber = {2841069},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2011__47_3_650_0}
}
Masamune, Jun; Uemura, Toshihiro. Conservation property of symmetric jump processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 3, pp. 650-662. doi : 10.1214/09-AIHP368. http://www.numdam.org/item/AIHPB_2011__47_3_650_0/

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