标题：Subordinators which are infinitely divisible w.r.t. time: Construction, properties, and simulation of max-stable sequences and infinitely divisible laws
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：2
页码：977-1005
DOI：10.30757/ALEA.v16-35
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The concept of a Lévy subordinator is generalized to a family of nondecreasingstochastic processes, which are parameterized in terms of two Bernsteinfunctions. Whereas the independent increments property is only maintained in theLévy subordinator special case, the considered family is always strongly infinitelydivisible with respect to time, meaning that a path can be represented in distributionas a finite sum with arbitrarily many summands of independent and identicallydistributed paths of another process. Besides distributional properties of the process,we present two applications to the design of accurate and efficient simulationalgorithms. First, each member of the considered family corresponds uniquely toan exchangeable max-stable sequence of random variables, and we demonstratehow the associated extreme-value copula can be simulated exactly and efficientlyfrom its Pickands dependence measure. Second, we show how one obtains differentseries and integral representations for infinitely divisible probability laws byvarying the parameterizing pair of Bernstein functions, without changing the lawof one-dimensional margins of the process. As a particular example, we present anexact simulation algorithm for compound Poisson distributions from the Bondessonclass, for which the generalized inverse of the distribution function of the associatedStieltjes measure can be evaluated accurately.
