Description
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many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material.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.
A systematic treatment of stable Levy processes and self-similar Markov processes, for graduate students and researchers in the field.
About the Author
Andreas E. Kyprianou was educated at the University of Oxford and University of Sheffield and is currently a professor of mathematics at the University of Bath. He has spent over 25 years working on the theory and application of path-discontinuous stochastic processes and has over 130 publications, including a celebrated graduate textbook on Levy processes. During his time in Bath, he co-founded and directed the Prob-L@B (Probability Laboratory at Bath), was PI for a multi-million-pound EPSRC Centre for Doctoral Training, and is currently the Director of the Bath Institute for Mathematical Innovation. Juan Carlos Pardo is a full professor at the department of Probability and Statistics at Centro de Investigacion en Matematicas (CIMAT). He was educated at the Universidad Nacional Autonoma de Mexico (UNAM) and Universite de Paris VI (Sorbonne Universite). He has spent over 13 years working on the theory and application of path-discontinuous stochastic processes and has more than 50 publications in these areas. During the academic year 2018-2019, he held the David Parkin visiting professorship at the University of Bath.
Reviews
'This treatise takes readers on a superb journey through the fascinating worlds of stable Levy processes and of a rich variety of further naturally related random processes. Andreas Kyprianou and Juan Carlos Pardo masterfully deploy an arsenal of techniques, which are already interesting on their own right, to reveal many classical or more recent high level results on the distributions of functionals and on the path behaviours stable processes. It is indeed remarkable that their methods lead to so many explicit formulas, some amazingly simple, some more complex. The authors should be praised for making accessible as a coherent whole a vast literature that has been developed over several decades, including the latest developments.' Jean Bertoin, University of Zurich
Book Information
ISBN 9781108480291
Author Andreas E. Kyprianou
Format Hardback
Page Count 484
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 870g
Dimensions(mm) 234mm * 156mm * 27mm
A systematic treatment of stable Levy processes and self-similar Markov processes, for graduate students and researchers in the field.
About the Author
Andreas E. Kyprianou was educated at the University of Oxford and University of Sheffield and is currently a professor of mathematics at the University of Bath. He has spent over 25 years working on the theory and application of path-discontinuous stochastic processes and has over 130 publications, including a celebrated graduate textbook on Levy processes. During his time in Bath, he co-founded and directed the Prob-L@B (Probability Laboratory at Bath), was PI for a multi-million-pound EPSRC Centre for Doctoral Training, and is currently the Director of the Bath Institute for Mathematical Innovation. Juan Carlos Pardo is a full professor at the department of Probability and Statistics at Centro de Investigacion en Matematicas (CIMAT). He was educated at the Universidad Nacional Autonoma de Mexico (UNAM) and Universite de Paris VI (Sorbonne Universite). He has spent over 13 years working on the theory and application of path-discontinuous stochastic processes and has more than 50 publications in these areas. During the academic year 2018-2019, he held the David Parkin visiting professorship at the University of Bath.
Reviews
'This treatise takes readers on a superb journey through the fascinating worlds of stable Levy processes and of a rich variety of further naturally related random processes. Andreas Kyprianou and Juan Carlos Pardo masterfully deploy an arsenal of techniques, which are already interesting on their own right, to reveal many classical or more recent high level results on the distributions of functionals and on the path behaviours stable processes. It is indeed remarkable that their methods lead to so many explicit formulas, some amazingly simple, some more complex. The authors should be praised for making accessible as a coherent whole a vast literature that has been developed over several decades, including the latest developments.' Jean Bertoin, University of Zurich
Book Information
ISBN 9781108480291
Author Andreas E. Kyprianou
Format Hardback
Page Count 484
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 870g
Dimensions(mm) 234mm * 156mm * 27mm
