Density and tails of unimodal convolution semigroups

By Krzysztof Bogdan, T. Grzywny, M. Ryznar. 2013

157 citations recorded by the source corpus.

We give sharp bounds for the isotropic unimodal probability convolution semigroups when their L\'evy-Khintchine exponent has Matuszewska indices strictly between 0 and 2.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68df5a4454ae3b1aeae070b426d72d9cf4dd7a11

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Citations in the corpus

Barriers, exit time and survival probability for unimodal Lévy processes (2013, methodology): “We refer to [10] for additional discussion.”
Stochastic flows for Lévy processes with Hölder drifts (2015, unknown): “Moreover, it follows from (15) in [3] that ν(dz) c0 φ(|z| −2) |z|d dz.”
Dirichlet heat kernel for unimodal Lévy processes (2014, methodology): “Here are further remarks from [9]: We have ψ ∈WLSC(α,θ,c) if and only if ψ(θ)/θ is comparable to a nondecreasing function on (θ,∞), and ψ ∈WUSC(α,θ,C) if and only if ψ(θ)/θ is comparable to a nonincreasing function on (θ,∞).”
Heat kernel estimates for subordinate Brownian motions (2015, background): “ estimate can be expressed just in terms of the Laplace exponent and its inverse function. Such type of estimate will continue to hold if the scaling of the process X is strictly between 0 and 2 (see [BGR14] and Corollary 1.3), but if the scaling fails to satisfy this condition we will see that diﬀe”
Gradient estimates of harmonic functions and transition densities for Levy processes (2013, background): “Under some further conditions (6)-(7) can be reversed ([2]).”
Estimates of transition densities and their derivatives for jump Lévy processes (2013, background): “ for some θ0 ∈ S we have µ(B(θ0,r) ∩ S) ≥ crγ−1, r ≤ 1/2, then p1(rθ0) ≥ c(1 + r) −α γ, r > 0. The estimates for more general L´evy processes were next obtained in [30, 31, 16, 19]. A recent paper [2] contains some estimates of densities for isotropic unimodal L´evy processes with L´evy-Khintchin”
A framework for fractional Hardy inequalities (2013, background): “Lehrbäck for helpful discussions and preprints of [5] and [23].”