On the properties of Laplace transform originating from one-sided Lévy stable laws

We consider the conventional Laplace transform of f(x), denoted by with . For we furnish the closed form expressions for the inverse Laplace transforms and . In both cases they involve definite integration with kernels which are appropriately rescaled one-sided Lévy stable probability distribution f...

Full description

Saved in:
Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 49; no. 6; pp. 65201 - 65210
Main Authors Penson, K A, Górska, K
Format Journal Article
LanguageEnglish
Published IOP Publishing 12.02.2016
Subjects
Condensed Matter
Laplace transform
one-sided Lévy stable distribution
Physics
special functions
Online AccessGet full text

Cover

More Information
Summary:We consider the conventional Laplace transform of f(x), denoted by with . For we furnish the closed form expressions for the inverse Laplace transforms and . In both cases they involve definite integration with kernels which are appropriately rescaled one-sided Lévy stable probability distribution functions , , . Since are exactly and explicitly known for rational , i.e. for with , , our results extend the known and tabulated case of to any rational . We examine the integral kernels of this procedure as well as the resulting two kinds of Lévy integral transformations.
Bibliography:JPhysA-103556.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/49/6/065201