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Stable Levy Processes via Lamperti-Type Representations (Hardcover)
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Stable Levy Processes via Lamperti-Type Representations (Hardcover)
Series: Institute of Mathematical Statistics Monographs
Expected to ship within 9 - 15 working days
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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unpublished material.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.
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