Conservation property of symmetric jump processes
The authors consider a conservation property of jump stochastic processes. The main result of the paper indicates that even if the volume grows rapidly the jump process should stay in the space under some conditions imposed on the frequency of jumps. Among examples of processes satisfying the propose dassumptions are processes with finite range jumping kernels or symmetric stable line jumping kernels and continuous time Markov chains. The line of reasoning is based on a perturbation method [\textit{R. L. Schilling} and \textit{T. Uemura}, Tohoku Math. J. (2) 59, No. 3, 401--422 (2007; Zbl 1141.31006)].
scientific article; zbMATH DE number 5956521
scientific article