Heat kernel upper bounds for jump processes and the first exit time

124 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Regularity results for nonlocal parabolic equations (2013, background): “A detailed study of off-diagonal upper bounds can be found in [4].”
Heat kernel estimates for jump processes of mixed types on metric measure spaces (2007, methodology): “) So for x ∈ Bn \ Nn, t ∈ [1, 2] and r ∈ (0, rn), P ( ρ(Y (n) t , x) ≥ r ) = ∫ Bn\B(x,r) p(t, x, y)μ(dy) ≤ c8 ∫ Bn\B(x,r) e−c9ρ(x,y)μ(dy) ≤ c10e−c11 , (4.”
Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2009, background): “Further results on two-sided heat kernel estimates and a version of the parabolic Harnack inequality for symmetric jump processes are contained in [2] and [3].”
A priori Holder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps (2008, methodology): “It uses some ideas previously developed in [2, 4, 8, 9, 7].”
Heat kernel estimates for the fractional Laplacian with Dirichlet conditions (2009, background): “Regarding other recent estimates [3, 17, 20, 23, 36] for the transition density and potential kernel of jumptype processes, we need to point out that generally these only concern processes without killing.”
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.”