Estimates of Green Function for Relativistic α-Stable Process

By M. Ryznar. 2002

151 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cbee373aedfa388c04c15f097b9a2ec68b6d4929

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Citations in the corpus

Gradient estimates of harmonic functions and transition densities for Levy processes (2013, background): “In particular, one of the processes satisfying the above conditions is the relativistic process in R with the Laplace exponent φ(λ) = √ λ+m2 −m, m > 0, and a generator m− √ m2 −Δ (see [7], [25], [21]).”
Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of L\'{e}vy processes (2012, unknown): “(5) Relativistic rotationally symmetric α-stable process [22, 71].”
Intrinsic Ultracontractivity for Schrödinger Operators Based on Fractional Laplacians (2009, unknown): “process [32].”
Dirichlet heat kernel estimates for Δα/2 + Δβ/2 (2010, unknown): “Let bx :=√ 1 + | ∇Γ(x̃)|2 and hx,p(y) := ( h(y) )p .”
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): “2) hold for all ∈ (0,2)? Besides the spherically symmetric stable processes, there are various other classes of Lévy processes, like the relativistic stable processes [15,29] and geometric stable processes [31], which also have widespread applications.”
Transition density estimates for jump Lévy processes (2010, unknown): “, in [30, 23, 15], and [5], we have ν(D) = c1 ∫”
Drift transforms and Green function estimates for discontinuous processes (2003, background): “For any bounded C 1;1 open set D in R n ; there is a constant C ¼ CðD; a; mÞ40 such that When D is a bounded C 1;1 -domain, Theorem 3.2 is the main result of Ryznar [27], which was proved in a different way there.”
Two‐sided Green function estimates for killed subordinate Brownian motions (2010, background): “The same form of the estimates in the case α = 2 (and d 3) were obtained much earlier in [31, 33] for the Brownian motion case.”
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]).”
Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators (2007, methodology): “of the relativistic operator ([10]), may be studied by a similar perturbation technique ([ 33 , 31, 19]).”
Estimates of Tempered Stable Densities (2008, background): “x|)ae−c3 |x ! (56) , x ∈ A, t ∈ (1,∞). We like to discuss the particular case of the relativistic α–stable L´evy process with Φm(ξ) = (|ξ|2 + m2/α)α/2 − m for m > 0 which is investigated, e.g., in [21], [16] and [11]. We consider here only m = 1 because pm t (x) = md/αp1 mt(m 1/αx), 21 where pm t”
Potential theory of truncated stable processes (2006, background): “Keywords and phrases: Green functions, Poisson kernels, truncated symmetric stable processes, symmetric stable processes, harmonic functions, Harnack inequality, boundary Harnack principle, Martin boundary.”