Journal ArticleDOI
Natural exponential families and self-decomposability
Reads0
Chats0
TLDR
In this article, it was shown that if a self-decomposable probability distribution is composed of selfdecompositionable elements, then the exponential dispersion model generated by the distribution shares the same property.About:
This article is published in Statistics & Probability Letters.The article was published on 1992-01-27. It has received 12 citations till now. The article focuses on the topics: Exponential dispersion model & Natural exponential family.read more
Citations
More filters
Journal ArticleDOI
Processes of normal inverse Gaussian type
TL;DR: A number of stochastic processes with normal inverse Gaussian marginals and various types of dependence structures are discussed, including Ornstein-Uhlenbeck type processes, superpositions of such processes and Stochastic volatility models in one and more dimensions.
Lévy Processes in Finance: Theory, Numerics, and Empirical Facts
TL;DR: In this article, Eberlein and Raible presented an extension of the Lévy term structure model to multivariate driving Léveys and stochastic volatility structures.
Posted Content
Modelling by Lévy Processes for Financial Econometrics
TL;DR: In this article, the use of positive Ornstein-Uhlenbeck (OU) type processes inside stochastic volatility processes is discussed in some detail, and the basic probability theory asso-ciated with such models is discussed.
Book ChapterDOI
Modelling by Lévy Processess for Financial Econometrics
TL;DR: In this paper, a review of recent work in which Levy processes are used to model and analyse time series from financial econometrics is presented. But the main feature of the paper is the use of posi- tive Ornstein-Uhlenbeck-type processes inside stochastic volatility processes.
Journal ArticleDOI
Processes of Meixner type
TL;DR: In this paper, the Esscher transforms of mixed Meixner processes are defined and characterized as Markov processes or semimartingales, and Ornstein-Uhlenbeck and self-similar processes of MeixNER type are also described.
References
More filters
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Journal ArticleDOI
Survival models for heterogeneous populations derived from stable distributions
TL;DR: In this article, a new three-parameter family of distributions on the positive numbers is proposed, which includes the stable distributions, the gamma, the degenerate and the inverse Gaussian distributions.
Journal ArticleDOI
Natural Exponential Families with Quadratic Variance Functions
TL;DR: The normal, Poisson, gamma, binomial, and negative binomial distributions are univariate natural exponential families with quadratic variance functions as mentioned in this paper, where the variance is at most a function of the mean.
Journal ArticleDOI
Unimodality of Infinitely Divisible Distribution Functions of Class $L$
TL;DR: In this paper, it was shown that all infinitely divisible distribution functions of class $L$ are unimodal, and that all distributions of class L$ are non-convex.