Displaying similar documents to “Jump processes, ℒ-harmonic functions, continuity estimates and the Feller property”

Conservation property of symmetric jump processes

Jun Masamune, Toshihiro Uemura (2011)

Annales de l'I.H.P. Probabilités et statistiques

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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.

Degenerate stochastic differential equations for catalytic branching networks

Sandra Kliem (2009)

Annales de l'I.H.P. Probabilités et statistiques

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Uniqueness of the martingale problem corresponding to a degenerate SDE which models catalytic branching networks is proven. This work is an extension of the paper by Dawson and Perkins [ (2006) 323–383] to arbitrary catalytic branching networks. As part of the proof estimates on the corresponding semigroup are found in terms of weighted Hölder norms for arbitrary networks, which are proven to be equivalent to the semigroup norm for this generalized setting.

On the coupling property of Lévy processes

René L. Schilling, Jian Wang (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall–Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component. ...

Symmetric jump processes : localization, heat kernels and convergence

Richard F. Bass, Moritz Kassmann, Takashi Kumagai (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.