Topics In Infinitely Divisible Distributions And L Vy Processes Revised Edition
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Topics In Infinitely Divisible Distributions And L Vy Processes Revised Edition
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Author : Alfonso Rocha-Arteaga
language : en
Publisher: Springer Nature
Release Date : 2019-11-02
Topics In Infinitely Divisible Distributions And L Vy Processes Revised Edition written by Alfonso Rocha-Arteaga and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-02 with Mathematics categories.
This book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions Lm, m = 0,1,...,∞, from the class L0 of selfdecomposable distributions to the class L∞ generated by stable distributions through convolution and convergence. The book is divided into five chapters. Chapter 1 studies basic properties of Lm classes needed for the subsequent chapters. Chapter 2 introduces Ornstein-Uhlenbeck type processes generated by a Lévy process through stochastic integrals based on Lévy processes. Necessary and sufficient conditions are given for a generating Lévy process so that the OU type process has a limit distribution of Lm class. Chapter 3 establishes the correspondence between selfsimilar additive processes and selfdecomposable distributions and makes a close inspection of the Lamperti transformation, which transforms selfsimilar additive processes and stationary type OU processes to each other. Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process. Finally, Chapter 5 studies strictly stable and Lm properties inherited by the subordinated process in multivariate subordination. In this revised edition, new material is included on advances in these topics. It is rewritten as self-contained as possible. Theorems, lemmas, propositions, examples and remarks were reorganized; some were deleted and others were newly added. The historical notes at the end of each chapter were enlarged. This book is addressed to graduate students and researchers in probability and mathematical statistics who are interested in learning more on Lévy processes and infinitely divisible distributions.
Perspectives In Mathematical Sciences
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Author : Yisong Yang
language : en
Publisher: World Scientific
Release Date : 2010
Perspectives In Mathematical Sciences written by Yisong Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
Gun Shy
Stochastic Analysis And Related Topics
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Author : Fabrice Baudoin
language : en
Publisher: Birkhäuser
Release Date : 2017-10-04
Stochastic Analysis And Related Topics written by Fabrice Baudoin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-04 with Mathematics categories.
The articles in this collection are a sampling of some of the research presented during the conference “Stochastic Analysis and Related Topics”, held in May of 2015 at Purdue University in honor of the 60th birthday of Rodrigo Bañuelos. A wide variety of topics in probability theory is covered in these proceedings, including heat kernel estimates, Malliavin calculus, rough paths differential equations, Lévy processes, Brownian motion on manifolds, and spin glasses, among other topics.
Fluctuations Of L Vy Processes With Applications
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Author : Andreas E. Kyprianou
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-09
Fluctuations Of L Vy Processes With Applications written by Andreas E. Kyprianou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
Monotonicity Properties Of Infinitely Divisible Distributions
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Author : B. G. Hansen
language : en
Publisher:
Release Date : 1990
Monotonicity Properties Of Infinitely Divisible Distributions written by B. G. Hansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Distribution (Probability theory). categories.
Cambridge Tracts In Mathematics
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Author : Jean Bertoin
language : en
Publisher: Cambridge University Press
Release Date : 1996
Cambridge Tracts In Mathematics written by Jean Bertoin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.
L Vy Processes And Stochastic Calculus
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Author : David Applebaum
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-30
L Vy Processes And Stochastic Calculus written by David Applebaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-30 with Mathematics categories.
Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Levy Flights And Related Topics In Physics
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Author : Michael F. Shlesinger
language : en
Publisher:
Release Date : 2014-01-15
Levy Flights And Related Topics In Physics written by Michael F. Shlesinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
L Vy Processes And Infinitely Divisible Distributions
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Author : Sato Ken-Iti
language : en
Publisher: Cambridge University Press
Release Date : 1999
L Vy Processes And Infinitely Divisible Distributions written by Sato Ken-Iti and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Distribution (Probability theory) categories.
Combinatorial Stochastic Processes
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Author : Jim Pitman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Combinatorial Stochastic Processes written by Jim Pitman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-11 with Mathematics categories.
The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.