On stochastic completeness of jump processes

By Alexander Grigorʼyan, Xueping Huang, J. Masamune. 2012

94 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ca4fdcb5cd7c560e43155de8903e260b59fba513

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Citations in the corpus

A note on self-adjoint extensions of the Laplacian on weighted graphs (2012, methodology): “In the context of stochastic completeness for jump processes see the work of Masamune/ Uemura [38], Grigor’yan/Huang/Masamune [20] and also [25, 26].”
Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory (2010, background): “ed in the last section. For related material concerning heat semigroup estimates we refer to reader to [31]. After this work was ﬁnished we learned about recent work of Grigor’yan, Huang and Masamune [11] on stochastic completeness, which seems to have some points of contact with our considerations.”
Two-sided estimates of heat kernels of jump type Dirichlet forms (2018, background): “However, the conservativeness of the Dirichlet form (E ,F) with the jump kernel J (x, y) ' d (x, y) with β < 2 follows from a result of [24], which finishes the proof.”
Estimates of heat kernels for non-local regular Dirichlet forms (2014, background): “If (E ,F) has only a jump part and 0 < β < 2, then (V≤) and (J≤) imply that (E ,F) is conservative (see [19, 35]).”
On the conservativeness and the recurrence of symmetric jump-diffusions (2012, methodology): “Now, we recall the standard adapted distance d in [15].”
Graphs of finite measure (2013, background): “d and ﬁrst studied systematically in [12] (see [51] for earlier appearances as well). Subsequently, they have become a main tool in certain geometric and spectral theoretic considerations, see, e.g., [2, 3, 10, 11, 18, 21, 24, 44, 45]. They are always deﬁned with respect to some measure m on X. In o”
Volume growth and stochastic completeness of graphs (2012, methodology): “We call a metric ρ adapted to the VSRW X on (Γ , π ) if there exists C ρ ≥ 0 such that for all x ∈ G , This condition has appeared previously in [10], [12], and [17], and it has apparently close connections to the condition in the deﬁnition of E X .”
Cheeger inequalities for unbounded graph Laplacians (2012, background): “[14, 15, 16, 23, 25, 30, 31, 32, 42], where certain variations of the concept also go under the name of adapted metrics.”