Topic
Subordinator
About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.
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TL;DR: In this paper, the scaling limit of a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail is shown to be a fractional kinetics process.
Abstract: We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit of this process is a Fractional-Kinetics process—that is the time change of a d-dimensional Brownian motion by the inverse of an independent α-stable subordinator. We further show that the same process appears in the scaling limit of the non-symmetric Bouchaud’s trap model.
68 citations
TL;DR: In this paper, a large class of subordinate Brownian motions X via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero and at infinity were considered.
68 citations
TL;DR: In this article, the authors studied the number of parts K n of a random composition and other related functionals under the assumption that R = Φ(S • ), where (S t, t ≥ 0) is a subordinator and Φ:[0,∞] → [0, 1] is a diffeomorphism.
Abstract: A random composition of n appears when the points of a random closed set R ⊂ [0,1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts K n of this composition and other related functionals under the assumption that R = Φ(S • ), where (S t , t ≥ 0) is a subordinator and Φ:[0,∞] → [0, 1] is a diffeomorphism. We derive the asymptotics of K n when the Levy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function Φ(x) = 1 - e -x , we establish a connection between the asymptotics of K n and the exponential functional of the subordinator.
67 citations
TL;DR: In this paper, the authors investigated the asymptotic behavior of (1 − G(x))−(Σ npn)(1 − F(x)), as x → ∞ if 1 − F is regularly varying with index ϱ, 0 ≤ ϱ ≤ 1.
65 citations
TL;DR: In this paper, the first-exit time of a tempered β-stable subordinator, also called inverse tempered stable (ITS) subordinator was investigated and the limiting form of the ITS density and its k-th order derivatives were derived as the space variable x → 0 +.
64 citations