Stable Lvy Processes via Lamperti-Type Representations (Hardcover)

Hardcover. Stable Levy processes lie at the intersection of Levy 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 Levy 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many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material.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. This completely new mathematical treatment, geared toward graduate students and researchers, systemically covers the theory of Stable Levy processes, which serve as a key building block to many other stochastic models prevalent in biology, physics, economics and engineering. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…