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Generalized Gamma Convolutions and Related Classes of Distributions and Densities
TLDR
In this paper, the authors provide a systematic account of the theory of generalized Gamma convolutions and related classes of probability distributions and densities, and several well-known probability distributions are treated in the accompanying examples.Citations
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Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics
TL;DR: The authors construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive Ornstein-Uhlenbeck (OU) processes, and study these models in relation to financial data and theory.
Journal ArticleDOI
Mittag-Leffler Functions and Their Applications
TL;DR: In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented and an attempt is made to present nearly an exhaustive list of references to make the reader familiar with the present trend of research in Mittag, Leffler, and type functions and their applications.
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Tempering stable processes
TL;DR: In this paper, the authors consider a general and robust class of multivariate tempered stable distributions and establish their identifiable parametrization and prove short and long time behavior of tempered stable Levy processes and investigate their absolute continuity with respect to the underlying α -stable processes.
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Mittag-Leffler Functions and Their Applications
TL;DR: A detailed survey of Mittag-Leffler type functions can be found in this article, where the authors present a detailed account or rather a brief survey of the Mittag Leffler function, generalized Mittag leffler functions and their interesting and useful properties.
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The Theory of Scale Functions for Spectrally Negative Lévy Processes
TL;DR: In this article, the authors give an up-to-date account of the theory and applications of scale functions for spectrally negative Levy processes, including the first extensive overview of how to work numerically with scale functions.