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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 , a stochastic model for the failure times of items subject to two external random shocks occurring as events in an underlying bivariate counting process is proposed, where the two kinds of shocks occur according to a bivariate space-fractional Poisson process.
Abstract: Abstract We propose a stochastic model for the failure times of items subject to two external random shocks occurring as events in an underlying bivariate counting process. This is a special formulation of the competing risks model, which is of interest in reliability theory and survival analysis. Specifically, we assume that a system, or an item, fails when the sum of the two types of shock reaches a critical random threshold. In detail, the two kinds of shock occur according to a bivariate space-fractional Poisson process, which is a two-dimensional vector of independent homogeneous Poisson processes time-changed by an independent stable subordinator. Various results are given, such as analytic hazard rates, failure densities, the probability that the failure occurs due to a specific type of shock, and the survival function. Some special cases and ageing notions related to the NBU characterization are also considered. In this way we generalize certain results in the literature, which can be recovered when the underlying process reduces to the homogeneous Poisson process.
TL;DR: In this paper , a self-standardized central limit theorem for trimmed subordinated subordinators is proved for the case of a subordinated sub-subordinate subordinator, which is the case for the usual trimmed subordinator and a closely related subordinated trim-subordinator.
Abstract: In this note, we prove self-standardized central limit theorems (CLTs) for trimmed subordinated subordinators. We shall see that there are two ways to trim a subordinated subordinator. One way leads to CLTs for the usual trimmed subordinator and a second way to a closely related subordinated trimmed subordinator and CLTs for it.
01 Jan 2014
TL;DR: This chapter is devoted to studying how the Wiener–Hopf factorisation can be used to characterise the behaviour of any Levy process at first passage over a fixed level.
Abstract: This chapter is devoted to studying how the Wiener–Hopf factorisation can be used to characterise the behaviour of any Levy process at first passage over a fixed level. The case of a subordinator will be excluded throughout this chapter, as this has been dealt with in Chap. 5. Nonetheless, the analysis of how subordinators make first passage will play a crucial role in understanding the case of a general Levy process.
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TL;DR: In this paper, the authors define a subordinator by means of the lower-incomplete gamma function, which can be considered as an approximation of the stable subordinator, easier to be handled thanks to its finite activity.
Abstract: We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also considered in order to overcome the drawback of infinite moments. Then, we study Levy processes time-changed by these subordinators, with particular attention to the Brownian case. An approximation of the fractional derivative (as well as of the fractional power of operators) arises from the analysis of governing equations. Finally, we show that time-changing the fractional Brownian motion gives a model of anomalous diffusion, which exhibits a sub-diffusive behavior.
TL;DR: In this paper, the authors introduce the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor set.
Abstract: We introduce the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor set. We also introduced an interesting and powerful technique to investigate the multifractal spectrum.