Stable Levy Processes via Lamperti-Type Representations

Stable Lévy processes are a combination of Lévy processes and self-similar Markov processes,and can be represented using Markov additive processes (MAPs). This book provides a mathematical treatment of stable Lévy processes,exploring topics such as first hitting laws,path conditionings,law-preserving path transformations,extremal points,growth envelopes,and winding behavior. It is written for graduate students and researchers in the field and includes both classical results and recent developments.

Format: Hardback
Length: 484 pages
Publication date: 07 April 2022
Publisher: Cambridge University Press

Stable Lévy processes, a fascinating realm that intersects Lévy processes and self-similar Markov processes, hold immense mathematical significance. These processes, belonging to the latter class, possess a remarkable representation known as the Lamperti-type, which arises through the space-time path transformation of Markov additive processes (MAPs). This groundbreaking mathematical approach harnesses the inherent properties of stable processes, allowing for an explicit description in one dimension and a semi-explicit description in higher dimensions. By leveraging this unique perspective, the book presents a comprehensive catalog of explicit results that vividly capture the intricate path fluctuations of stable Lévy processes across one and higher dimensions. Authored with graduate students and researchers in mind, this comprehensive text systematically establishes numerous classical results while also introducing numerous recent breakthroughs, many of which have remained unpublished until now. The diverse range of topics explored includes first hitting laws for diverse sets, path conditionings, law-preserving path transformations, the distribution of extremal points, growth envelopes, and winding behavior. Each chapter is meticulously crafted to provide a clear and concise understanding of these complex concepts, making it an invaluable resource for scholars and practitioners alike.

Weight: 874g
Dimension: 159 x 234 x 31 (mm)
ISBN-13: 9781108480291
Edition number: New ed