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Author: Andreas E. Kyprianou Publisher: Springer Science & Business Media ISBN: 3540313435 Category : Mathematics Languages : en Pages : 382
Book Description
This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. 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 transparency and explicitness.
Author: Andreas E. Kyprianou Publisher: Springer Science & Business Media ISBN: 3540313435 Category : Mathematics Languages : en Pages : 382
Book Description
This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. 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 transparency and explicitness.
Author: Andreas E. Kyprianou Publisher: Springer Science & Business Media ISBN: 3642376320 Category : Mathematics Languages : en Pages : 461
Book Description
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.
Author: Oleg Kudryavtsev Publisher: ISBN: 9781536195255 Category : Lévy processes Languages : en Pages : 0
Book Description
"Lâevy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Lâevy process in finance is the Black-Scholes model. This book presents important financial applications of Lâevy processes. The Editors consider jump-diffusion and pure non-Gaussian Lâevy processes, the multi-dimensional Black-Scholes model, and regime-switching Lâevy models. This book is comprised of seven chapters that focus on different approaches to solving applied problems under Lâevy 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: Krzysztof Dębicki Publisher: Springer ISBN: 3319206931 Category : Mathematics Languages : en Pages : 256
Book Description
The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
Author: Serge Cohen Publisher: Springer ISBN: 9783642314063 Category : Mathematics Languages : en Pages : 186
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: Robert Dalang Publisher: Springer Science & Business Media ISBN: 3034800215 Category : Mathematics Languages : en Pages : 487
Book Description
This volume contains refereed research or review papers presented at the 6th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, in May 2008. The seminar focused mainly on stochastic partial differential equations, especially large deviations and control problems, on infinite dimensional analysis, particle systems and financial engineering, especially energy markets and climate models. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance.
Author: Catherine Donati-Martin Publisher: Springer Nature ISBN: 3030964094 Category : Mathematics Languages : en Pages : 399
Book Description
This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs. The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.
Author: Andreas E. Kyprianou
Author: Andreas E. Kyprianou
Author: Andreas E. Kyprianou
Author: Andreas E. Kyprianou
Author: Oleg Kudryavtsev
Author: Krzysztof Dębicki
Author: 
Author: Serge Cohen
Author: David Applebaum
Author: Robert Dalang
Author: Catherine Donati-Martin