Lévy Matters III - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Matters III write by Björn Böttcher. This book was released on 2014-01-16. Lévy Matters III available in PDF, EPUB and Kindle. 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.
Lévy Matters II
Lévy Matters II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Matters II write by Serge Cohen. This book was released on 2012-09-14. Lévy Matters II available in PDF, EPUB and Kindle. 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.
Lévy Matters VI
Lévy Matters VI - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Matters VI write by Franziska Kühn. This book was released on 2017-10-05. Lévy Matters VI available in PDF, EPUB and Kindle. Presenting some recent results on the construction and the moments of Lévy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Applications range from heat kernel estimates for a class of Lévy-type processes to existence and uniqueness theorems for Lévy-driven stochastic differential equations with Hölder continuous coefficients. Moreover, necessary and sufficient conditions for the existence of moments of Lévy-type processes are studied and some estimates on moments are derived. Lévy-type processes behave locally like Lévy processes but, in contrast to Lévy processes, they are not homogeneous in space. Typical examples are processes with varying index of stability and solutions of Lévy-driven stochastic differential equations. This is the sixth 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.
Lévy Matters V
Lévy Matters V - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Matters V write by Lars Nørvang Andersen. This book was released on 2015-10-24. Lévy Matters V available in PDF, EPUB and Kindle. This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier. If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.
Lévy Matters IV
Lévy Matters IV - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Matters IV write by Denis Belomestny. This book was released on 2014-12-05. Lévy Matters IV available in PDF, EPUB and Kindle. The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Lévy processes. These days, statistics for stochastic processes is a lively topic, driven by the needs of various fields of application, such as finance, the biosciences, and telecommunication. The three chapters of this volume are completely dedicated to the estimation of Lévy processes, and are written by experts in the field. The first chapter by Denis Belomestny and Markus Reiß treats the low frequency situation, and estimation methods are based on the empirical characteristic function. The second chapter by Fabienne Comte and Valery Genon-Catalon is dedicated to non-parametric estimation mainly covering the high-frequency data case. A distinctive feature of this part is the construction of adaptive estimators, based on deconvolution or projection or kernel methods. The last chapter by Hiroki Masuda considers the parametric situation. The chapters cover the main aspects of the estimation of discretely observed Lévy processes, when the observation scheme is regular, from an up-to-date viewpoint.
