Drift transforms and Green function estimates for discontinuous processes

By Zhen-Qing Chen, Renming Song. 2003

84 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ace77eb455d6ed66f4c1edd3de5e49a683cfffd6

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Citations in the corpus

Harnack inequality for some classes of Markov processes (2004, background): “A relativistic α-stable process is a L´ evy processes whose infinitesimal generator can be written as m − (− + m 2/α ) α/2 ,0 4 ] or [12] for details.”
Stochastic flows for Lévy processes with Hölder drifts (2015, background): “(For some basic information on symmetric relativistic α-stable processes, one refers to, for instance, [2, Chapter 5] or [4].”
Boundary Harnack principle for subordinate Brownian motions (2007, background): “These processes can be regarded as perturbations of rotationally invariant stable processes and their Green functions on bounded smooth domains are comparable to their counterparts for rotationally invariant stable processes (see [9], [22], [12], [15], [16] and [17]).”
Green Function Estimates and Harnack Inequality for Subordinate Brownian Motions (2006, unknown): “In the first case the Lévy measure is given by ðtÞ 1⁄4 cð Þt 1 , in the second case by ðtÞ 1⁄4 t (1)e , and in the third case by ðtÞ 1⁄4 cð Þe t 1 =2 (see, for instance, [10] or [18]), where cð Þ 1⁄4 ð =2Þ= ð1 =2Þ.”
Two-sided eigenvalue estimates for subordinate processes in domains (2005, background): “7) of[15], the Dirichlet form forX is (E ,W /2,2(Rd)) and there is a constant c5 > 1 such that c−1 5 E1(u, u) E 1 (u, u) c5 E1(u, u) for u ∈ W /2,2(Rd), where(E,W /2,2(Rd)) is the Dirichlet form for the spherical symmetric -stable process in R .”
Potential theory of truncated stable processes (2006, methodology): “In [25,16], sharp estimates on the Green functions of killed relativistic stable processes in bounded C1,1 domains were established.”
Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators (2007, methodology): “We refer the interested reader to the work of Chen and Song [36, 37, 12, 13 ], Bogdan and Byczkowski [3, 4], and Takeda and Uemura [38, 40, 39].”
Heat kernel estimates for jump processes of mixed types on metric measure spaces (2007, unknown): “It is shown in [12] that the corresponding jumping intensity satisfies J(x, y) 3 Ψ(m|x− y|) |x− y|d+α , where Ψ(r) 3 e−r(1 + r(d+α−1)/2) near r = ∞, and Ψ(r) = 1 + Ψ′′(0)r2/2 + o(r4) near r = 0.”
Corrigendum to “Global heat kernel estimates for symmetric jump processes” (2011, unknown): “It is shown in [14] that the corresponding jumping intensity is J(x, y) = Ψα(m|x− y|) |x− y|d+α , where Ψα(r) is decreasing and Ψα(r) is asymptotically equal to e−r(1 + r(d+α−1)/2) near r = ∞, and Ψα(r) = 1 + Ψ′′ α(0)r(2)/2 + o(r(4)) near r = 0.”
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes (2013, unknown): “142] that the Lévy exponent of the truncated α-stable process is comparable to that of the relativistic α-stable process, but the Lévy densities are not comparable (for estimates on the Lévy density of the relativistic α-stable process, see [20]).”
Two‐sided Green function estimates for killed subordinate Brownian motions (2010, methodology): “The results of Kim, Song and Vondraček [19] are reproved in [20] under conditions of this paper (with the redundant assumptions removed).”
Uniqueness of stable processes with drift (2013, background): “This is because Y is a purely discontinuous Lévy process and so the effect of a Girsanov transform can only produce a purely discontinuous “drift term”; see [5, 6].”