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 article, the authors examined the continuous-time autoregressive moving average process driven by α-stable Levy motion delayed by inverse stable subordinator for high-frequency data with visible jumps and so-called "trapping-events".
Abstract: In this paper we examine the continuous-time autoregressive moving average process driven by α -stable Levy motion delayed by inverse stable subordinator. This process can be applied to high-frequency data with visible jumps and so-called “trapping-events”. Those properties are often visible in financial time series but also in amorphous semiconductors, technical data describing the rotational speed of a machine working under various load regimes or data related to indoor air quality. We concentrate on the main characteristics of the examined subordinated process expressed in the language of the measures of dependence which are main tools used in statistical investigation of real data. However, because the analyzed system is based on the α -stable distribution therefore we cannot consider here the correlation (or covariance) as a main measure which indicates at the dependence inside the process. In the paper we examine the codifference, the more general measure of dependence defined for wide class of processes. Moreover we present the simulation procedure of the considered system and indicate how to estimate its parameters. The theoretical results we illustrate by the simulated data analysis.
15 citations
••
TL;DR: In this article, the authors study solutions of a class of higher-order partial differential equations in bounded domains, where the authors express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index 0 < β < 1, or by the absolute value of a symmetric α-stable process with 0 < α ≤ 2.
Abstract: We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Allouba and Zheng \cite{allouba1}, Baeumer, Meerschaert and Nane \cite{bmn-07}, Meerschaert, Nane and Vellaisamy \cite{MNV}, and Nane \cite{nane-h}. We express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index $0<\beta <1$, or by the absolute value of a symmetric $\alpha$-stable process with $0<\alpha\leq 2$, independent of the Markov process. In some special cases we represent the solutions by running composition of $k$ independent Brownian motions, called $k$-iterated Brownian motion for an integer $k\geq 2$. We make use of a connection between fractional-time diffusions and higher order partial differential equations established first by Allouba and Zheng \cite{allouba1} and later extended in several directions by Baeumer, Meerschaert and Nane \cite{bmn-07}.
15 citations
•
TL;DR: In this article, the authors give explicit solutions for fractional diffusion problems on bounded domains, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of the fractional time derivative.
Abstract: This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of the fractional time derivative. Some applications are given, to demonstrate how to specify a well-posed Dirichlet problem for space-time fractional diffusions in one or several variables. This solves an open problem in numerical analysis.
15 citations
••
TL;DR: In this paper, the authors revisited Hunt's hypothesis (H) and Getoor's conjecture for Levy processes and showed that X satisfies H if and only if the equation A y = − a − ∫ { x ∈ R n ∖ A R n : | x | 1 } x μ (d x ), y ∈ r n, has at least one solution.
14 citations
•
TL;DR: In this paper, the existence of the density associated to the exponential functional of the Levy process was studied and it was shown that the density of the function satisfies an integral equation that generalizes the one found by Carmona et al.
Abstract: In this paper, we study the existence of the density associated to the exponential functional of the Levy process $\xi$, \[ I_{\ee_q}:=\int_0^{\ee_q} e^{\xi_s} \, \mathrm{d}s, \] where $\ee_q$ is an independent exponential r.v. with parameter $q\geq 0$. In the case when $\xi$ is the negative of a subordinator, we prove that the density of $I_{\ee_q}$, here denoted by $k$, satisfies an integral equation that generalizes the one found by Carmona et al. \cite{Carmona97}. Finally when $q=0$, we describe explicitly the asymptotic behaviour at 0 of the density $k$ when $\xi$ is the negative of a subordinator and at $\infty$ when $\xi$ is a spectrally positive Levy process that drifts to $+\infty$.
14 citations