TY  - BOOK
AU  - Kyprianou,Andreas E.
AU  - Pardo,Juan Carlos
TI  - Stable LÃ©vy processes via Lamperti-type representations
T2  - Institute of Mathematical Statistics monographs
SN  - 9781108648318 (ebook)
AV  - QA274.73 .K975 2022
U1  - 519.2/82 23
PY  - 2022///
CY  - Cambridge
PB  - Cambridge University Press
KW  - LÃ©vy processes
KW  - Stochastic processes
N1  - Title from publisher's bibliographic system (viewed on 23 Mar 2022)
N2  - Stable LÃ©vy processes lie at the intersection of LÃ©vy 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 LÃ©vy 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many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material.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
UR  - https://doi.org/10.1017/9781108648318
ER  -