{"product_id":"stable-levy-processes-via-lamperti-type-representations-hardback-9781108480291","title":"Stable Lévy Processes via Lamperti-Type Representations (Hardback) 9781108480291","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eStable Lévy Processes via Lamperti-Type Representations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA systematic treatment of stable Lévy processes and self-similar Markov processes, for graduate students and researchers in the field.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAndreas E. Kyprianou (Author), Juan Carlos Pardo (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108480291, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 7 April 2022\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e484 pages\u003cbr\u003e23.4 x 15.6 x 2.7 cm, 0.87 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This treatise takes readers on a superb journey through the fascinating worlds of stable Lévy 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\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eStable Lévy processes lie at the intersection of Lévy 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 Lévy 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Stable distributions\u003cbr\u003e 2. Lévy processes\u003cbr\u003e 3. Stable processes\u003cbr\u003e 4. Hypergeometric Lévy processes\u003cbr\u003e 5. Positive self-similar Markov processes\u003cbr\u003e 6. Spatial fluctuations in one dimension\u003cbr\u003e 7. Doney–Kuznetsov factorisation and the maximum\u003cbr\u003e 8. Asymptotic behaviour for stable processes\u003cbr\u003e 9. Envelopes of positive self-similar Markov processes\u003cbr\u003e 10. Asymptotic behaviour for path transformations\u003cbr\u003e 11. Markov additive and self-similar Markov processes\u003cbr\u003e 12. Stable processes as self-similar Markov processes\u003cbr\u003e 13. Radial reflection and the deep factorisation\u003cbr\u003e 14. Spatial fluctuations and the unit sphere\u003cbr\u003e 15. Applications of radial excursion theory\u003cbr\u003e 16. Windings and up-crossings of stable processes\u003cbr\u003e Appendix.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46266360070424,"sku":"9781108480291","price":48.85,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781108480291i.jpg?v=1696706056","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/stable-levy-processes-via-lamperti-type-representations-hardback-9781108480291","provider":"Freshly Printed Books","version":"1.0","type":"link"}