Topic
Subordinator
About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors give the "quenched" scaling limit of Bouchaud's trap model in d ≥ 2, i.e., the time change of a d-dimensional Brownian motion by the inverse of an independent α-stable subordinator.
Abstract: We give the "quenched" scaling limit of Bouchaud's trap model in d ≥ 2. This scaling limit is the fractional-kinetics process, that is the time change of a d-dimensional Brownian motion by the inverse of an independent α-stable subordinator.
81 citations
01 Feb 2011
TL;DR: In this article, the semigroup property of Fokker-planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion is investigated.
Abstract: In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered is the first hitting time process for either a stable subordinator or a mixture of stable subordinators. A family of operators arising in the representation of the Fokker-Plank-Kolmogorov equations is shown to have the semigroup property.
80 citations
TL;DR: In this paper, the authors prove that the Harnack inequality is valid for the nonnegative harmonic functions of X, obtained by subordinating Brownian motion with a subordinator with a positive drift.
Abstract: Let X be a Levy process in
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq% WIDesOdaahaaWcbeqaaiaadsgaaaaaaa!3A16!
$$\mathbb{R}^{d} $$
, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca% WGKbGaeyyzImRaaG4maaaa!3AFC!
$$d \geqslant 3$$
, obtained by subordinating Brownian motion with a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a Levy process with no continuous component. We study the asymptotic behavior of the Green function of X near zero. Under the assumption that the Laplace exponent of the subordinator is a complete Bernstein function we also describe the asymptotic behavior of the Green function at infinity. With an additional assumption on the Levy measure of the subordinator we prove that the Harnack inequality is valid for the nonnegative harmonic functions of X.
78 citations
[...]
TL;DR: A parametric family of n-dimensional extreme-value copulas of Marshall-Olkin type is introduced and is shown to share some properties with Archimedean copulas regarding construction and analytical form.
78 citations