Transition Probabilities for Symmetric Jump Processes

By Richard F. Bass, David A. Levin. 2002

166 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1cf5b83b0fa93a71dd65d62355edb597201de015

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Citations in the corpus

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.”
Non-local dirichlet forms and symmetric jump processes (2006, background): “Harnack inequalities for non-local operators have been considered in [BL02a] and [SV04] for fixed order, non-symmetric operators, [BL02b] and [CK03] for fixed order, symmetric operators.”
Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order (2005, methodology): “For a study of symmetric jump processes under similar assumptions see Bass and Levin (2002b) and Chen and Kumagai (2003).”
Heat kernel upper bounds for jump processes and the first exit time (2009, background): “A number of previous papers have obtained heat kernel upper bounds for jump processes under similar conditions – see in particular [3, 5, 13].”
A priori estimates for integro-differential operators with measurable kernels (2009, methodology): “Using the approach of [ BL02b ] H¨older regularity is proved in [CK03] in a framework which is similar to ours; extensions may be found [CK06].”
Regularity for parabolic integro-differential equations with very irregular kernels (2014, result): “The first estimate for parabolic integro-differential equations, in non-divergence form, appeared, to the best of our knowledge, in [36] (the divergence case had some earlier results such as [3], [16]).”
Heat kernels for non-symmetric diffusion operators with jumps (2016, background): “v [22] obtained two-sided heat kernel estimatesfor certain stable-like processes in Rd, whose inﬁnitesimal generators are a class of pseudo-diﬀerential operators having smooth symbols. Bass and Levin [2] used a completely diﬀerent approach to obtain similar estimates for discrete time Markov chain o”
Local Regularity for Parabolic Nonlocal Operators (2012, methodology): “For time-independent kernels the article [3] establishes a Harnack inequality and Hölder regularity estimates with the use of methods both from probability and analysis.”
Weighted Poincaré inequality and heat kernel estimates for finite range jump processes (2008, background): “Bass and Levin [4] used a completely different approach to obtain similar estimates for discrete time Markov chain on Zd where the conductance between x and y is comparable to |x−y|−d−α forα ∈ (0, 2).”
Green Function Estimates and Harnack Inequality for Subordinate Brownian Motions (2006, background): “In their work, Bass and Levin [4] established upper and lower bounds on the transition densities of symmetric Markov chains on the integer lattice in d dimensions, where the conductance between x and y is comparable to jx yjdþ , 2 ð0; 2Þ.”
Potential Theory of Subordinate Brownian Motion (2009, methodology): “The same method was also used in [5] and [16] to prove a parabolic Harnack inequality.”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, unknown): “There are also many important results in this direction including [17], [60], [16], [15], [57], [22], [58], [13], [12], [19], [23], [25], [47], [26], [42] and [56].”
Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2009, methodology): “Two-sided heat kernel estimates for a class of stable-like processes in Rn were obtained by Kolokoltsov [29]; Bass and Levin [4] used a completely different approach to get transition density estimates for discrete time Markov chains in Zd with certain conductance.”
Estimates of heat kernels for non-local regular Dirichlet forms (2014, methodology): “The techniques for obtaining heat kernel bounds for non-local Dirichlet forms have been developed by a number of authors; see for example [4,6,7,9,10] and the references therein.”
Stability of heat kernel estimates for symmetric non-local Dirichlet forms (2016, methodology): “s≤ c r2 φ(r) for r>0. (1.7) For α-stable-like processes where φ(r) = rα, condition (1.7) corresponds exactly to 0 <α<2. Some of the key methods used in [CK1] were inspired by a previous work [BL] on random walks on integer lattice Zd. The notion of d-set arises in the theory of function spa”
Corrigendum to “Global heat kernel estimates for symmetric jump processes” (2011, background): “When X is a pure jump symmetric process on Z or R whose jumping kernel is of stable or mixed stable type (that decays polynomially at infinity), sharp estimates on p(t, x, y) have been derived in [4] (on Z) and in [12, 13] (on”
A new formulation of Harnack?s inequality for nonlocal operators (2011, unknown): “A priori estimates in Hölder spaces for similar Dirichlet forms have been obtained in [8,2,4] and other works.”