On the inverse gamma subordinator
TLDR
In this article , the moments of the inverse gamma subordinator and the governing equations associated with Gamma subordinators and inverse processes are given in terms of higher transcendental functions, also known as Volterra functions.Abstract:
In this paper we deal with some open problems concerned with Gamma subordinators. In particular, we first provide a representation for the moments of the inverse gamma subordinator. Then, we focus on λ-potentials and we study the governing equations associated with Gamma subordinators and inverse processes. Such representations are given in terms of higher transcendental functions, also known as Volterra functions. read more
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On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint
TL;DR: In this article , the authors provide a short introduction of new and well-known facts relating non-local operators and irregular domains. And they consider Cauchy problems and boundary value problems, which lead to anomalous behavior on the bulk and on the surface of a given domain, respectively.
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The Variance Gamma Process and Option Pricing
TL;DR: In this article, a three-parameter stochastic process, termed the variance gamma process, is developed as a model for the dynamics of log stock prices, which is obtained by evaluating Brownian motion with drift at a random time given by a gamma process.
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Mittag-Leffler Functions, Related Topics and Applications
TL;DR: In this article, the authors present a self-contained, comprehensive treatment of the theory of the Mittag-Leffler functions, ranging from rather elementary matters to the latest research results, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena.
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A First Course in Sobolev Spaces
TL;DR: Leoni as discussed by the authors takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable.