Conservation property of symmetric jump processes

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On stochastic completeness of jump processes (2012, unknown): “In a similar setting Masamune and Uemura [ 26 ] proved the stochastic completeness under a stronger hypothesis than (7): for any e> 0”
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].”
On the conservativeness and the recurrence of symmetric jump-diffusions (2012, background): “We note that this model manifold M does not satisfy the volume tests in [26, 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”
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]).”
Volume growth and stochastic completeness of graphs (2012, background): “Criteria for stochastic completeness in the general setting of symmetric jump processes are proved in [27].”