Potential Analysis of Stable Processes and its Extensions

By Krzysztof Bogdan, T. Byczkowski, Tadeusz Kulczycki, M. Ryznar, Renming Song, Zoran Vondraček, Piotr Graczyk, A. Stos. 2009

282 citations recorded by the source corpus.

Subfields: Finance, Management, Monitoring, Policy and Law, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7c3b93f1c185e7f0eec43b8adfa24c051019afbb

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Citations in the corpus

What is the fractional Laplacian? A comparative review with new results (2018, background): “In general, the probabilistic literature on stable-type processes in bounded domains and related notions of fractional Laplacians is very rich [94].”
Two‐sided Green function estimates for killed subordinate Brownian motions (2010, methodology): “n motion corresponding to φ 3 is the sum of a symmetric α-stable process and an independent symmetric β-stable process. The subordinate Brownian motions corresponding to φ 4 and φ 5 were discussed in [6]. In the case d ≥ 3, the only condition on the complete Bernstein function φis (1.2), so we can u”
Large $s$-harmonic functions and boundary blow-up solutions for the fractional Laplacian (2013, result): “[5] Krzysztof Bogdan, Tomasz Byczkowski, Tadeusz Kulczycki, Michal Ryznar, Renming Song, and Zoran Vondraček.”
Ten equivalent definitions of the fractional laplace operator (2015, methodology): “It was heavily used, for example, in hydrodynamics [22, 23, 28, 31], and, more recently, in probability theory [1, 2, 8, 32].”
Suprema of Lévy processes (2011, background): “The recent progress in the potential theory of Lévy processes is, in part, due to the application of fluctuation theory, see [9, 10, 18, 22, 23, 24, 25].”
Stochastic flows for Lévy processes with Hölder drifts (2015, background): “On the other hand, when d = 1 and Z is a symmetric α-stable process in R with α ∈ [1, 2), it is shown in [22] that pathwise uniqueness holds for (1.”
Fractional Laplacian with Hardy potential (2017, unknown): “3) It is well-known [26] that p1ðxÞ 1 jxj d , hence pt x ð Þ t d=a t jxjdþa ; t>0; x 2 R: (2.”