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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Dissertation•
14 Jun 2004
TL;DR: In this article, the authors construct random intervals from the partial records of a Poisson point process and characterize its law via the potential measure of the subordinator associated to the set.
Abstract: This thesis is composed of two parts. The first deals with the construction of a random set which has the property of regeneration. Precisely, we construct random intervals from the partial records of a Poisson point process; these are used to partially cover $\mathbb(R)^+.$ The purpose of this work is to study the random set $\Rs$ that is left uncovered. We give integral tests to decide whether the random set $\Rs$ has a positive Lebesgue measure, has isolated points or if it is bounded. We show that $\Rs$ is, indeed, a regenerative set and characterize its law via the potential measure of the subordinator associated to $\Rs$. We obtain formulas to estimate some fractal dimensions of $\Rs.$ The second part consists of some contributions to the theory of positive self--similar Markov processes. To obtain the results of this part, we use Lamperti's transformation which establishes a bijection between this class of processes and real--valued Levy processes. Firstly, we are interested in the behavior at infinity of increasing self--similar Markov processes. In this vein, under some hypotheses, we find a deterministic function $f$ such that the liminf, as $t$ goes to infinity, of the quotient $X_t/f(t)$ is finite and different from 0 with probability $1.$ We obtain an analogous result which determines the behavior near of 0 of the process $X$ started from 0. Secondly, we study the different ways to construct a positive self--similar Markov process $\widetilde(X)$ for which 0 is a regular and recurrent point. To this end, we give some conditions that enable us to ensure that a such process exists and to determine its resolvent. Next, we make a systematic study of the Ito excursion measure $\exc$ of the process $\widetilde(X)$. In particular, we give a description of $\exc$ similar to that of Imhof for Ito's excursion measure of Brownian motion; we determine the law under $\exc$ of the normalized excursion and the image under time reversal of $\exc$. Furthermore, we construct and describe a process which is in weak duality with the process $\widetilde(X).$ We obtain some estimations of tail probabilities of the law of an exponential functional of a Levy process.
Posted Content•
TL;DR: In this paper, the convergence of the probability density function as the Hurst index was studied for the fractional Ornstein-Uhlenbeck process with a time-changed version, obtained via an inverse α-stable subordinator.
Abstract: We consider the fractional Ornstein-Uhlenbeck process, solution of a stochastic differential equation driven by the fractional Brownian motion, and we study its time-changed version, obtained via an inverse $\alpha$-stable subordinator We focus on the convergence of the probability density function as the Hurst index $H \to \frac{1}{2}$ The generalized fractional Fokker-Planck equation for such process is introduced and the class of subordinated solutions of such equation is studied, providing some uniqueness and isolation results and studying the convergence as $H \to \frac{1}{2}$
TL;DR: The authors explored contextual factors around these two causal markers, incorporating the effective factors in multifactorial models to measure their weights in discriminating between these two markers, and examined the different weights borne by individual factors from the perspective of markedness correspondence strategies.
30 Mar 2023
TL;DR: In this article , the authors studied the Poisson process time-changed by independent L'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma-subordinator and tempered incomplete gamma subordinator, and derived their distributional properties such as probability mass function, mean, variance, correlation, tail probabilities and fractional moments.
Abstract: In this paper, we study the Poisson process time-changed by independent L\'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive their important distributional properties such as probability mass function, mean, variance, correlation, tail probabilities and fractional moments. The long-range dependence property of these processes are discussed. An application in insurance domain is studied in detail. Finally, we present the likelihood plots, the pdf plots and the simulated sample paths for the subordinators and their corresponding subordinated Poisson processes.
TL;DR: In this paper , the spectral heat content for time-changed killed Brownian motions on open sets was investigated for either a subordinator or an inverse subordinator, with the underlying Laplace exponent being regularly varying at $$\infty $$ with index $$\beta \in (0,1)$$ .
Abstract: The spectral heat content is investigated for time-changed killed Brownian motions on $$C^{1,1}$$ open sets, where the time change is given by either a subordinator or an inverse subordinator, with the underlying Laplace exponent being regularly varying at $$\infty $$ with index $$\beta \in (0,1)$$ . In the case of inverse subordinators, the asymptotic limit of the spectral heat content in small time is shown to involve a probabilistic term depending only on $$\beta \in (0,1)$$ . In contrast, in the case of subordinators, this universality holds only when $$\beta \in (\frac{1}{2}, 1)$$ .