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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Stable Lévy Processes Via Lamperti-Type Representations

Stable Lévy Processes Via Lamperti-Type Representations

Kyprianou, Andreas E.
Pardo, Juan Carlos

Hardcover

Series: Institute of Mathematical Statistics Monographs, Book 7

Probability & Statistics

ISBN10: 1108480292
ISBN13: 9781108480291
Publisher: Cambridge University Press
Published: Apr 7 2022
Pages: 484
Weight: 1.95
Height: 1.00 Width: 6.20 Depth: 9.30
Language: English
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many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material.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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