Author: Andreas E. Kyprianou
Publisher: Cambridge University Press
ISBN: 1108572162
Category : Mathematics
Languages : en
Pages : 486
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Book Description
Stable 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many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material.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.
Author: Jean Bertoin
Publisher:
ISBN:
Category : Lévy processes
Languages : en
Pages : 265
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Author: Björn Böttcher
Publisher: Springer
ISBN: 3319026844
Category : Mathematics
Languages : en
Pages : 215
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Book Description
This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is a counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.
Author: Jean Bertoin
Publisher: Cambridge University Press
ISBN: 9780521562430
Category : Mathematics
Languages : en
Pages : 275
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Book Description
This is an up-to-date and comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin has used the powerful interplay between the probabilistic structure (independence and stationarity of the increments) and analytic tools (especially Fourier and Laplace transforms) to give a quick and concise treatment of the core theory, with the minimum of technical requirements. Special properties of subordinators are developed and then appear as key features in the study of the local times of real-valued Lévy processes and in fluctuation theory. Lévy processes with no positive jumps receive special attention, as do stable processes. In sum, this will become the standard reference on the subject for all working probability theorists.
Author: Serge Cohen
Publisher: Springer
ISBN: 3642314074
Category : Mathematics
Languages : en
Pages : 200
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Book Description
This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two important topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.
Author: Joshua D. Rushton
Publisher:
ISBN:
Category :
Languages : en
Pages : 96
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Book Description
Author: Oleg Kudryavtsev
Publisher: Nova Science Publishers
ISBN: 9781536198492
Category : Mathematics
Languages : en
Pages : 259
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Book Description
"Lévy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Lévy process in finance is the Black-Scholes model. This book presents important financial applications of Lévy processes. The Editors consider jump-diffusion and pure non-Gaussian Lévy processes, the multi-dimensional Black-Scholes model, and regime-switching Lévy models. This book is comprised of seven chapters that focus on different approaches to solving applied problems under Lévy processes: Monte Carlo simulations, machine learning, the frame projection method, dynamic programming, the Fourier cosine series expansion, finite difference schemes, and the Wiener-Hopf factorization. Various numerical examples are carefully presented in tables and figures to illustrate the methods designed in the book"--
Author: Franciscus Johannes De Weert
Publisher:
ISBN:
Category :
Languages : en
Pages : 79
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Author: Svetlana Boyarchenko
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Integral representations for expectations of functions of a stable L 'evy process $X$ and its supremum $ bar X$ are derived. As examples, cumulative probability distribution functions (cpdf) of $X_T, barX_T$, the joint cpdf of $X_T$ and $ barX_T$, and the expectation of $( be X_T- barX_T)_+$, $ be>1$, are considered, and efficient numerical procedures for cpdfs are developed. The most efficient numerical methods use the conformal acceleration technique and simplified trapezoid rule.
Author: Jean Bertoin
Publisher:
ISBN: 9787510005091
Category : Lévy processes
Languages : en
Pages : 266
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Book Description
