Lévy Processes: Theory and Applications
A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of shastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior.

This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch.

The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, shastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

1116897951
Lévy Processes: Theory and Applications
A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of shastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior.

This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch.

The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, shastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

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Lévy Processes: Theory and Applications

Lévy Processes: Theory and Applications

Lévy Processes: Theory and Applications

Lévy Processes: Theory and Applications

Overview

A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of shastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior.

This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch.

The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, shastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

Product Details

ISBN-13: 9780817641672
Publisher: Birkhäuser Boston
Publication date: 03/30/2001
Edition description: 2001
Pages: 418
Product dimensions: 7.01(w) x 10.00(h) x 0.28(d)

Table of Contents

I. A Tutorial on Levy Processes.- Basic Results on Lévy Processes.- II. Distributional, Pathwise, and Structural Results.- Exponential Functionals of Lévy Processes.- Fluctuation Theory for Lévy Processes.- Gaussian Processes and Local Times of Symmetric Lévy Processes.- Temporal Change in Distributional Properties of Lévy Processes.- III. Extensions and Generalizations of Lévy Processes.- Lévy Processes in Shastic Differential Geometry.- Lévy-Type Processes and Pseudodifferential Operators.- Semistable Distributions.- IV. Applications in Physics.- Analytic and Probabilistic Aspects of Lévy Processes and Fields in Quantum Theory.- Lévy Processes and Continuous Quantum Measurements.- Lévy Processes in the Physical Sciences.- Some Properties of Burgers Turbulence with White or Stable Noise Initial Data.- V. Applications in Finance.- Modelling by Lévy Processess for Financial Econometrics.- Application of Generalized Hyperbolic Lévy Motions to Finance.- Explicit Form and Path Regularity of Martingale Representations.- Interpretations in Terms of Brownian and Bessel Meanders of the Distribution of a Subordinated Perpetuity.- VI. Numerical and Statistical Aspects.- Maximum Likelihood Estimation and Diagnostics for Stable Distributions.- Series Representations of Lévy Processes from the Perspective of Point Processes.
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