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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: A model based on the continuous time autoregressive time series with stable noise delayed by the infinitely divisible inverse subordinator is proposed which can be used for description of subdiffusion processes of real data.
Abstract: Many real data exhibit behavior adequate to subdiffusion processes. Very often it is manifested by so-called “trapping events”. The visible evidence of subdiffusion we observe not only in financial time series but also in technical data. In this paper we propose a model which can be used for description of such kind of data. The model is based on the continuous time autoregressive time series with stable noise delayed by the infinitely divisible inverse subordinator. The proposed system can be applied to real datasets with short-time dependence, visible jumps and mentioned periods of stagnation. In this paper we extend the theoretical considerations in analysis of subordinated processes and propose a new model that exhibits mentioned properties. We concentrate on the main characteristics of the examined subordinated process expressed mainly in the language of the measures of dependence which are main tools used in statistical investigation of real data. We present also the simulation procedure of the considered system and indicate how to estimate its parameters. The theoretical results we illustrate by the analysis of real technical data.
12 citations
01 Jan 2008
TL;DR: In this article, the Laplace exponent Φ of A and the covering number of a set K ⊂ [0, ∞] were derived for the Gamma process, where A is a subordinator and K is a self-similar set.
Abstract: Let A = ` A(t) ́ t0 be a subordinator. Given a compact set K ⊂ [0,∞) we prove two-sided estimates for the covering numbers of the random set {A(t) : t ∈ K} which depend on the Laplace exponent Φ of A and on the covering numbers of K. This extends former results in the case K = [0, 1]. Using this we find the behavior of the small deviation probabilities for subordinated processes ` WH ` A(t) ́ ́ t∈K , where WH is a fractional Brownian motion with Hurst index 0 < H < 1. The results are valid in the quenched as well as in the annealed case. In particular, those questions are investigated for Gamma processes. Here some surprising new phenomena appear. As application of the general results we find the behavior of log P (supt∈K |Zα(t)| < ε) as ε→ 0 for the α-stable Lévy motion Zα. For example, if K is a self-similar set with Hausdorff dimension D > 0, then this behavior is of order −ε−αD in complete accordance with the Gaussian case α = 2. 2000 AMS Mathematics Subject Classification: Primary: 60G51; Secondary: 60G15, 60G52, 28A80, 60G18.
12 citations
TL;DR: In this article, the authors show that the fractionally integrated inverse stable subordinator (FIISS) is a scaling limit in the Skorokhod space of a renewal shot noise process with heavy-tailed, infinite mean "inter-shot" distribution and regularly varying response function.
12 citations
TL;DR: In this article, a multistable subordinator is introduced to generalize the stable subordinator to the case of time-varying stability index, which enables the convergence of a continuous-time random walk to the multifractional Poisson process.
12 citations
TL;DR: Using inverse subordinators and Mittag-Leffler functions, this paper presented a new definition of a fractional Poisson process parametrized by points of the Euclidean space.
Abstract: Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space $\mathbb{R}_+^2$
. Some properties are given and, in particular, we prove a long-range dependence property.
12 citations