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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: In this paper, it was shown that there exists a stable Levy motion and a self-decomposable subordinator, such that the corresponding subordinated process X ( T ( t ), t ⩾ 0 ) is not selfdecompositionable.
9 citations
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TL;DR: In this paper, the authors study non-homogeneous versions of the space-fractional and the time-frractional Poisson processes, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. The authors consider the Poisson process time-changed by H and obtain its explicit distribution and governing equation.
Abstract: The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable replaced by a stable subordinator and its inverse, respectively. The aim of this paper is to study non-homogeneous versions of such models, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. Firstly, we consider the Poisson process time-changed by H and we obtain its explicit distribution and governing equation. Then, by using the right-continuous inverse of H, we define an inhomogeneous analogue of the time-fractional Poisson process.
9 citations
TL;DR: In this article, the semi-implicit Euler-Maruyama (EM) method is investigated to approximate a class of time-changed stochastic differential equations, whose drift coefficient can grow super-linearly and diffusion coefficient obeys the global Lipschitz condition.
Abstract: The semi-implicit Euler–Maruyama (EM) method is investigated to approximate a class of time-changed stochastic differential equations, whose drift coefficient can grow super-linearly and diffusion coefficient obeys the global Lipschitz condition. The strong convergence of the semi-implicit EM is proved and the convergence rate is discussed. When the Bernstein function of the inverse subordinator (time-change) is regularly varying at zero, we establish the mean square polynomial stability of the underlying equations. In addition, the numerical method is proved to be able to preserve such an asymptotic property. Numerical simulations are presented to demonstrate the theoretical results.
9 citations
TL;DR: In this article, the authors consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass and prove that the sequence (F2(m,F3(m),…) converges in distribution, with respect to the Skorohod topology, to a fragmentation with immigration process.
Abstract: We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let F1(m)(t),F2(m)(t),… denote the decreasing rearrangement of the masses present at time t in a such process, starting from an initial mass m. Let then m→∞. Under an assumption of regular variation type on the dynamics of the fragmentation, we prove that the sequence (F2(m),F3(m),…) converges in distribution, with respect to the Skorohod topology, to a fragmentation with immigration process. This holds jointly with the convergence of m−F1(m) to a stable subordinator. A continuum random tree counterpart of this result is also given: the continuum random tree describing the genealogy of a self-similar fragmentation satisfying the required assumption and starting from a mass converging to ∞ will converge to a tree with a spine coding a fragmentation with immigration.
8 citations
TL;DR: This work derives some distributional properties of the multivariate generalized shot-noise process and obtains transforms pertaining to the joint stationary arrival rate and queue length processes, as well as their means and covariance structure for a network of infinite-server queues.
Abstract: We consider a network of infinite-server queues where the input process is a Cox process of the following form: The arrival rate is a vector-valued linear transform of a multivariate generalized (i.e., being driven by a subordinator rather than a compound Poisson process) shot-noise process. We first derive some distributional properties of the multivariate generalized shot-noise process. Then these are exploited to obtain the joint transform of the numbers of customers, at various time epochs, in a single infinite-server queue fed by the above-mentioned Cox process. We also obtain transforms pertaining to the joint stationary arrival rate and queue length processes (thus facilitating the analysis of the corresponding departure process), as well as their means and covariance structure. Finally, we extend to the setting of a network of infinite-server queues.
8 citations