Levy Processes

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many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material.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 e

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

This volume presents recent developments in the area of Levy-type processes and more general stochastic processes that behave locally like a Levy process. Although written in a survey style, quite a f

?This book covers Levy processes and their applications in the contexts of reliability and storage. Special attention is paid to life distributions and the maintenance of devices subject to degradatio

Levy 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

In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis

Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein–Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark–Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduat

The financial crisis that began in the summer of 2007 has led to criticisms that the financial models used by risk managers, portfolio managers, and even regulators simply do not reflect the realitie

This book is an introductory guide to using Levy processes for credit risk modelling. It covers all types of credit derivatives: from the single name vanillas such as Credit Default Swaps (CDSs) right

While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important

This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This scho

Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of L?vy processes has also seen many exciting developments. T

Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Lévy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer.

This three-chapter volume concerns the distributions of certain functionals of Levy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal di

This book presents basic stochastic processes, stochastic calculus including Levy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential con

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distribution

Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.

This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with indepen

This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tem

The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Levy processes. These days, statistics for stochastic processes is a lively

Stable Levy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theo

The essays in this anthology study Israeli television, its different forms of representation, audiences and production processes, past and present, examining Israeli television in both its local, cult

The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of Hille–Yosida and Lumer–Phillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and Feller–Markov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the Riemann–Liouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash i

The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of Hille–Yosida and Lumer–Phillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and Feller–Markov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the Riemann–Liouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash i

Statistical mechanics has been proven to be successful at describing physical systems at thermodynamic equilibrium. Since most natural phenomena occur in nonequilibrium conditions, the present challenge is to find suitable physical approaches for such conditions: this book provides a pedagogical pathway that explores various perspectives. The use of clear language, and explanatory figures and diagrams to describe models, simulations and experimental findings makes the book a valuable resource for undergraduate and graduate students, and also for lecturers organizing teaching at varying levels of experience in the field. Written in three parts, it covers basic and traditional concepts of nonequilibrium physics, modern aspects concerning nonequilibrium phase transitions, and application-orientated topics from a modern perspective. A broad range of topics is covered, including Langevin equations, Levy processes, directed percolation, kinetic roughening and pattern formation.

The book provides an extensive introduction to queueing models driven by Levy-processes as well as a systematic account of the literature on Levy-driven queues. The objective is to make the reader fam

This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Levy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitativ

This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy p

This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given.

This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given.

Neuroscience has dramatically increased understanding of how mental states and processes are realized by the brain, thus opening doors for treating the multitude of ways in which minds become dysfunctional. This book explores questions such as when is it permissible to alter a person's memories, influence personality traits or read minds? What can neuroscience tell us about free will, self-control, self-deception and the foundations of morality? The view of neuroethics offered here argues that many of our new powers to read ,alter and control minds are not entirely unparalleled with older ones. They have, however, expanded to include almost all our social, political and ethical decisions. Written primarily for graduate students, this book will appeal to anyone with an interest in the more philosophical and ethical aspects of the neurosciences.

This book contains 18 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Levy processes, stochastic control and optimization problems, st

This state-of-the-art reference provides current and effective disease-specific strategies for the management of patients receiving mechanical ventilation-emphasizing weaning processes, monitored seda

The book assesses the impact of core political and social institutions on regulatory structures and performance in the telecommunications industry in Jamaica, the United Kingdom, Chile, Argentina, and the Philippines. These core institutions are shown to influence strongly the credibility and effectiveness of regulation, and thus its ability to encourage private investment and support efficiency. Currently, privatization and regulatory reform are often viewed as the solution to the problem of poor performance by telecommunications and other public utilities. This volume argues that these high expectations may not always be met because of the way a country's political and social institutions - its executive, legislative and judicial systems, its informal norms of public behaviour - interact with regulatory processes and economic conditions. In some environments, regulatory solutions run counter to the prevailing wisdom: achieving credible commitment may require an inflexible regulatory

The book assesses the impact of core political and social institutions on regulatory structures and performance in the telecommunications industry in Jamaica, the United Kingdom, Chile, Argentina, and the Philippines. These core institutions are shown to influence strongly the credibility and effectiveness of regulation, and thus its ability to encourage private investment and support efficiency. Currently, privatization and regulatory reform are often viewed as the solution to the problem of poor performance by telecommunications and other public utilities. This volume argues that these high expectations may not always be met because of the way a country's political and social institutions - its executive, legislative and judicial systems, its informal norms of public behaviour - interact with regulatory processes and economic conditions. In some environments, regulatory solutions run counter to the prevailing wisdom: achieving credible commitment may require an inflexible regulatory

Conceived as the successor to Gregg and Steinberg's Cognitive Processes in Writing, this book takes a multidisciplinary approach to writing research. The authors describe their current thinking and da

Divided into four sections this text researchs the interaction between stress and neuroimmunological processes and the implications of these stress effects to human conditions such as Post Traumatic S