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Stable Lévy processes via Lamperti-type representations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stable Lévy processes via Lamperti-type representationsAndreas E. Kyprianou, Juan Carlos Pardo.
Author:	Kyprianou, Andreas E.
other author:	Pardo, Juan Carlos.
Published:	Cambridge :Cambridge University Press,2022.
Description:	xx, 463 p. :ill., digital ;24 cm.
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$q(electronic bk.)

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

Stable Lévy processes via Lamperti-type representations[electronic resource] /Andreas E. Kyprianou, Juan Carlos Pardo. - Cambridge :Cambridge University Press,2022. - xx, 463 p. :ill., digital ;24 cm. - 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many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material.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$q(electronic bk.)Subjects--Topical Terms:

377498
Lévy processes.

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

Dewey Class. No.: 519.282

Stable Lévy processes via Lamperti-type representations
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300 $a xx, 463 p. : $b ill., digital ; $c 24 cm.
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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.
650 0 $a Lévy processes. $3 377498
650 0 $a Stochastic processes. $3 181874
700 1 $a Pardo, Juan Carlos. $3 819224
830 0 $a Institute of Mathematical Statistics monographs. $3 930625
856 4 0 $u https://doi.org/10.1017/9781108648318