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Stable Lévy processes via Lamperti-type representations /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stable Lévy processes via Lamperti-type representations // Andreas E. Kyprianou, Juan Carlos Pardo.
Author:	Kyprianou, Andreas E.,
other author:	Pardo, Juan Carlos,
Description:	1 online resource (xx, 463 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 23 Mar 2022).
Subject:	Lévy processes. -
Online resource:	https://doi.org/10.1017/9781108648318
ISBN:	9781108648318 (ebook)

Stable Lévy processes via Lamperti-type representations /
Kyprianou, Andreas E.,

Stable Lévy processes via Lamperti-type representations /Andreas E. Kyprianou, Juan Carlos Pardo. - 1 online resource (xx, 463 pages) :digital, PDF file(s). - Institute of Mathematical Statistics monographs. - Institute of Mathematical Statistics monographs..

Title from publisher's bibliographic system (viewed on 23 Mar 2022).

Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov processes. Processes in the latter class enjoy a Lamperti-type representation as the space-time path transformation of so-called Markov additive processes (MAPs). This completely new mathematical treatment takes advantage of the fact that the underlying MAP for stable processes can be explicitly described in one dimension and semi-explicitly described in higher dimensions, and uses this approach to catalogue a large number of explicit results describing the path fluctuations of stable Lévy processes in one and higher dimensions. Written for graduate students and researchers in the field, this book systemically establishes many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material. Topics explored include first hitting laws for a variety of sets, path conditionings, law-preserving path transformations, the distribution of extremal points, growth envelopes and winding behaviour.

ISBN: 9781108648318 (ebook)Subjects--Topical Terms:

1405890
Lévy processes.

LC Class. No.: QA274.73 / .K975 2022

Dewey Class. No.: 519.2/82

Stable Lévy processes via Lamperti-type representations /
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500 $a Title from publisher's bibliographic system (viewed on 23 Mar 2022).
520 $a Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov processes. Processes in the latter class enjoy a Lamperti-type representation as the space-time path transformation of so-called Markov additive processes (MAPs). This completely new mathematical treatment takes advantage of the fact that the underlying MAP for stable processes can be explicitly described in one dimension and semi-explicitly described in higher dimensions, and uses this approach to catalogue a large number of explicit results describing the path fluctuations of stable Lévy processes in one and higher dimensions. Written for graduate students and researchers in the field, this book systemically establishes many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material. Topics explored include first hitting laws for a variety of sets, path conditionings, law-preserving path transformations, the distribution of extremal points, growth envelopes and winding behaviour.
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