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 paper, the authors developed extreme value theory for random observations separated by random waiting times whose exceedence probability falls off like a power law, and the resulting limit distributions were shown to be solutions of fractional differential equations, where the order of the fractional time derivative coincides with the power law index of the waiting time.
23 citations
TL;DR: In this article, an empirical type estimator of the Laplace transform of the EDPF was proposed and the asymptotic behavior of the estimator under a high frequency assumption was investigated.
Abstract: We consider a generalized risk process which consists of a subordinator plus a spectrally negative Levy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.
23 citations
TL;DR: In this paper, the variance generalised gamma convolution class of Levy processes formed by subordinating Brownian motion with Thorin subordinators is further extended using weak subordination, which is an extension of both univariate and multivariate subordination.
Abstract: Subordinating a multivariate Levy process, the subordinate, with a univariate subordinator gives rise to a pathwise construction of a new Levy process, provided the subordinator and the subordinate are independent processes. The variance-gamma model in finance was generated accordingly from a Brownian motion and a gamma process. Alternatively, multivariate subordination can be used to create Levy processes, but this requires the subordinate to have independent components. In this paper, we show that there exists another operation acting on pairs $(T,X)$ of Levy processes which creates a Levy process $X\odot T$. Here, $T$ is a subordinator, but $X$ is an arbitrary Levy process with possibly dependent components. We show that this method is an extension of both univariate and multivariate subordination and provide two applications. We illustrate our methods giving a weak formulation of the variance-$\boldsymbol{\alpha}$-gamma process that exhibits a wider range of dependence than using traditional subordination. Also, the variance generalised gamma convolution class of Levy processes formed by subordinating Brownian motion with Thorin subordinators is further extended using weak subordination.
23 citations
TL;DR: In this article, the authors derived a general criterion for the convergence of clock processes in random dynamics in random environments that is applicable in cases when correlations are not negligible, extending recent results by Gayrard [(2010), (2011), forthcoming], based on general criterion of convergence of sums of dependent random variables due to Durrett and Resnick [Ann. Probab. 6 (1978) 829-846].
Abstract: We derive a general criterion for the convergence of clock processes in random dynamics in random environments that is applicable in cases when correlations are not negligible, extending recent results by Gayrard [(2010), (2011), forthcoming], based on general criterion for convergence of sums of dependent random variables due to Durrett and Resnick [Ann. Probab. 6 (1978) 829-846]. We demonstrate the power of this criterion by applying it to the case of random hopping time dynamics of the p-spin SK model. We prove that on a wide range of time scales, the clock process converges to a stable subordinator almost surely with respect to the environment. We also show that a time-time correlation function converges to the arcsine law for this subordinator, almost surely. This improves recent results of Ben Arous, Bovier and Cerny [Comm. Math. Phys. 282 (2008) 663-695] that obtained similar convergence results in law, with respect to the random environment.
22 citations
TL;DR: In this paper, an empirical type estimator of the Laplace transform of the EDPF is presented, and the asymptotic behavior of the estimator under a high frequency assumption is investigated.
Abstract: We consider a generalized risk process which consists of a subordinator plus a spectrally negative Levy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF, and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.
22 citations