Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book provides the reader with comprehensive basic knowledge of Lévy processes, and at the same time introduces stochastic processes in general. No specialist knowledge is assumed and proofs and exercises are given in detail. The author systematically studies stable and semi-stable processes and emphasizes the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will benefit from this volume.
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"This book is a work of scrupulous scholarship, and an impressively detailed compendium of knowledge." Mathematical Reviews
Book Description
Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book provides the reader with comprehensive basic knowledge of Lévy processes, and at the same time serves as a n introduction to stochastic processes in general. The author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions, and treats many special subclasses such as stable or semi-stable processes. All serious students of random phenomena will find that this book has much to offer.
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First Sentence:
In this chapter we give basic definitions concerning probability spaces, stochastic processes, and Levy processes, and describe the main properties of characteristic functions, which we use in this book systematically. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dependent distributional property, generating triplet, homogeneous transition function, selfdecomposable distribution, leftmost mode, stationary independent increments property, strong unimodality, divisible distribution functions, unimodal with mode, convolution factor, continuous sample functions, infinitely divisible probability measures, bounded continuous density, strongly continuous contraction semigroup, accroissements indépendants, divisible distributions, infinitely divisible distribution, stochastic continuity, continuous singular, stable subordinator, jumping times, factorization identities, symmetric stable processes, modal interval, bigger tail New!
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In this chapter we give basic definitions concerning probability spaces, stochastic processes, and Levy processes, and describe the main properties of characteristic functions, which we use in this book systematically. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dependent distributional property, generating triplet, homogeneous transition function, selfdecomposable distribution, leftmost mode, stationary independent increments property, strong unimodality, divisible distribution functions, unimodal with mode, convolution factor, continuous sample functions, infinitely divisible probability measures, bounded continuous density, strongly continuous contraction semigroup, accroissements indépendants, divisible distributions, infinitely divisible distribution, stochastic continuity, continuous singular, stable subordinator, jumping times, factorization identities, symmetric stable processes, modal interval, bigger tail New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 60
books:
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- Selected Papers: Volume II (Contemporary Mathematicians) by S. Kakutani in Back Matter (1), and Back Matter (2)
- Limit Theorems of Probability Theory (Encyclopaedia of Mathematical Sciences) by Yu.V. Prokhorov in Back Matter (1), and Back Matter (2)
- Total Positivity, Volume One by Samuel Karlin in Back Matter
- Random Processes with Independent Increments (Mathematics and its Applications) by A.V. Skorohod in Back Matter
- Modelling Extremal Events: for Insurance and Finance (Stochastic Modelling and Applied Probability) by Paul Embrechts in Back Matter
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