Subordinator

About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.

Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex

Abstract: The Poisson-Kingman distributions, $\mathrm{PK}(\rho)$, on the infinite simplex, can be constructed from a Poisson point process having intensity density $\rho$ or by taking the ranked jumps up till a specified time of a subordinator with L\'evy density $\rho$, as proportions of the subordinator. As a natural extension, we replace the Poisson point process with a negative binomial point process having parameter $r>0$ and L\'evy density $\rho$, thereby defining a new class $\mathrm{PK}^{(r)}(\rho)$ of distributions on the infinite simplex. The new class contains the two-parameter generalisation $\mathrm{PD}(\alpha, \theta)$ of Pitman and Yor (1997) when $\theta>0$. It also contains a class of distributions derived from the trimmed stable subordinator. We derive properties of the new distributions, with particular reference to the two most well-known $\mathrm{PK}$ distributions: the Poisson-Dirichlet distribution $\mathrm{PK}(\rho_\theta)$ generated by a Gamma process with L\'evy density $\rho_\theta(x) = \theta e^{-x}/x$, $x>0$, $\theta > 0$, and the random discrete distribution, $\mathrm{PD}(\alpha,0)$, derived from an $\alpha$-stable subordinator.

A Functional Limit Theorem for stochastic integrals driven by a time-changed symmetric \alpha-stable L\'evy process

Abstract: Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the M_1-topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed symmetric \alpha-stable L\'evy process. The time change is given by the inverse \beta-stable subordinator.

Estimating the time value of ruin in a Lévy risk model under low-frequency observation

Abstract: In this paper, we consider statistical estimation of the time value of ruin in a Lévy risk model. Suppose that the aggregate claims process of an insurance company is modeled by a pure jump Lévy subordinator, and we can observe the data set on the aggregate claims based on low-frequency sampling. The time value of ruin is estimated by the Fourier-cosine method, and the uniform convergence rate is also derived. Through a lot of simulation studies, we show that our estimators are very effective when the sample size is finite.

Lévy-walk-like Langevin dynamics affected by a time-dependent force.

Abstract: The L\'evy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influence of external potentials at almost any time and anywhere. In this paper, we establish a Langevin system coupled with a subordinator to describe the L\'evy walk in a time-dependent periodic force field. The effects of external force are detected and carefully analyzed, including the nonzero first moment (even though the force is periodic), adding an additional dispersion on the particle position, a consistent influence on the ensemble- and time-averaged mean-squared displacement, etc. Besides, the generalized Klein-Kramers equation is obtained, not only for the time-dependent force but also for the space-dependent one.