Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Conservation property of symmetric jump processes

Jun Masamune and Toshihiro Uemura

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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 examples de processus satisfaisant ces conditions.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 47, Number 3 (2011), 650-662.

First available in Project Euclid: 23 June 2011

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Zentralblatt MATH identifier

Primary: 60J75: Jump processes 31C25: Dirichlet spaces 35R09: Integro-partial differential equations [See also 45Kxx]

Conservation property Symmetric Dirichlet forms with jumps Derivation property


Masamune, Jun; Uemura, Toshihiro. Conservation property of symmetric jump processes. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 3, 650--662. doi:10.1214/09-AIHP368.

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