کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4669082 1346102 2009 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration
چکیده انگلیسی

We first introduce and derive some basic properties of a two-parameters (α,γ)(α,γ) family of one-sided Lévy processes, with 1<α<21<α<2 and γ>−αγ>−α. Their Laplace exponents are given in terms of the Pochhammer symbol as followsψ(γ)(λ)=c((λ+γ)α−(γ)α),λ⩾0, where c   is a positive constant, (λ)α=Γ(λ+α)Γ(λ) stands for the Pochhammer symbol and Γ for the Gamma function. These are a generalization of the Brownian motion, since in the limit case α→2α→2, we end up to the Laplace exponent of a Brownian motion with drift γ+12. Then, we proceed by computing the density of the law of the exponential functional associated to some elements of this family (and their dual) and some transformations of these elements. More precisely, we shall consider the Lévy processes which admit the following Laplace exponent, for any δ>α−1α,ψ(0,δ)(λ)=ψ(0)(λ)−αδλ+α−1ψ(0)(λ),λ⩾0. These densities are expressed in terms of the Wright hypergeometric functions. By means of probabilistic arguments, we derive some interesting properties enjoyed by these functions. On the way, we also characterize explicitly the semi-group of the family of self-similar continuous state branching processes with immigration.

RésuméNous introduisons et étudions quelques propriétés élémentaires d'une famille de processus de Lévy complètement asymmétriques. Leurs lois sont caractérisées par leurs exposants de Laplace qui s'expriment en termes du symbole de Pochhammer. Ensuite, nous calculons la loi de la fonctionnelle exponentielle associée à certains éléments de cette famille et d'une tranformation de ces éléments. Ces lois s'avèrent absolument continues et leurs densités s'expriment en termes des fonctions hypergéométriques de Wright. En utilisant des arguments probabilistes, nous déduisons que ces fonctions possèdent des propriétés analytiques intéressantes. Lors du déroulement de la preuve, nous caractérisons également le semi-groupe des processus auto-similaires de branchement avec immigration.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 133, Issue 4, May 2009, Pages 355–382
نویسندگان
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