Harnack’s Inequality for Stable Lévy Processes

By Krzysztof Bogdan, Paweł Sztonyk. 2005

63 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5cbb6d904593119f20096a948f7ae715b82b3639

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In Applied Mathematics

In Finance

Citations in the corpus

Regularity for parabolic integro-differential equations with very irregular kernels (2014, background): “There is in fact a counterexample in [8] (also discussed in [24]).”
On Kelvin Transformation (2006, background): “By scaling (15) (see also (55) below), continuity of uλ and (43) Px(σ0=∞) = P x(σ0=∞)<1−uλ( x)/uλ(0)→0.”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, background): “This fact is well documented and there are counterexamples (see [20]).”
The best constant in a fractional Hardy inequality (2008, background): “In particular, we expect that the results of [16], [17] may be used to obtain, for the anisotropic stable [9], [10] censored processes, the ruin probabilities generalizing [7, Theorem 5.”
Harnack inequalities for subordinate Brownian motions (2012, methodology): “Our approach in obtaining pointwise estimates of Green function of balls uses maximum principle for certain operators (in a similar way as in [4]).”
On Harnack Inequality and Hölder Regularity for Isotropic Unimodal Lévy Processes (2013, background): “Note that similar condition as (A1) appeared in [4] and [1] and exactly the same in [5] and [6].”
Regularity theory for general stable operators (2014, background): “1), or related ones, has been widely investigated; see the works by Bass, Kassmann, Schwab, Silvestre, Sztonyk, and Bogdan, among others [1, 23, 22, 3, 39, 21, 2, 37, 5, 6, 7, 9, 24].”
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian (2005, methodology): “We note that Uφ(x) = lim r↓0 Urφ(x) is the Dynkin characteristic operator, which was used in [18] in a similar way.”
Fractional powers of second order partial differential operators: extension problem and regularity theory (2010, methodology): “1) la teor a se desarroll o en los ultimos a~ nos usando un enfoque probabil stico [6, 7, 10, 11, 12, 14, 44, 71], v ease tambi en el libro de K.”
Heat kernel estimates for jump processes of mixed types on metric measure spaces (2007, background): “See also [3, 4, 5, 7, 8, 21, 22] for related Harnack inequalities, Hölder continuity of harmonic functions and the Feller property for non-local operators.”
Boundary regularity for fully nonlinear integro-differential equations (2014, background): “This is important when considering non translation invariant equations for which a comparison principle for viscosity solutions is not available.”