Heat kernel estimates for jump processes of mixed types on metric measure spaces

By Zhen-Qing Chen, Takashi Kumagai. 2007

329 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/489d9aa4f4688357a16a7296861403eeb3b6cb42

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In Applied Mathematics

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Citations in the corpus

Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2009, result): “further extended these results to symmetric jump-type processes on metric measure spaces [11].”
Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps (2007, methodology): “This has been proved in the context of Markov processes on Zd and on d-sets in [BL, CK, CK2 ].”
Dirichlet heat kernel estimates for Δα/2 + Δβ/2 (2010, background): “The function ψ plays an important role in the study of mixed stable-like processes including X in [13], which serves as the ‘scale function’ for the heat kernel estimates and global parabolic Harnack inequality.”
A priori estimates for integro-differential operators with measurable kernels (2009, methodology): “Using the approach of [6] Holder regularity is proved in [7] in a framework which is similar to ours; extensions may be found [ 8 ].”
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes (2013, unknown): “We first recall the following from [9, 19].”
Heat kernel estimates for subordinate Brownian motions (2015, methodology): “For pure jump symmetric processes with stable-like jumping kernels on Z or R sharp heat kernel estimates were obtained in [2, 8, 10], while in [6, 15, 16, 19, 28] they were obtained for some classes of Lévy processes.”
Corrigendum to “Global heat kernel estimates for symmetric jump processes” (2011, methodology): “(Short time heat kernel estimates for relativistic stable processes were obtained in [13].”
A priori Holder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps (2008, methodology): “Under the above condition, a priori Hölder estimate and parabolic Harnack principle are established in [9] for parabolic functions of X.”
Estimates of transition densities and their derivatives for jump Lévy processes (2013, background): “Bounds for the transition density of a class of Markov processes with jump intensities which are not necessarily translation invariant but dominated by the Lévy measure of the stable rotation invariant process were given in [5, 6, 15].”
Boundary Harnack principle for Δ+Δ^{/2} (2012, background): “: (See, for example [ 8 ], Appendix A.) The purpose of this paper is to establish the following scale invariant version of the boundary”
Estimates of heat kernels for non-local regular Dirichlet forms (2014, methodology): “Moreover, if both condition (V ) (that is, V (x, r) r) and condition (J) (that is, J(x, y) d(x, y)−(α+β)) hold, then (UE) is true without any further hypothesis; see [9, 10].”
Dirichlet forms and associated heat kernels on the Cantor set induced by random walks on trees (2010, background): “This heat kernel estimate is a variant of that studied in Chen-Kumagai[3] and satisfies a typical asymptotic behavior of jump processes.”