This is an up-to-date and comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin has used the powerful interplay between the probabilistic structure (independence and stationarity of the increments) and analytic tools (especially Fourier and Laplace transforms) to give a quick and concise treatment of the core theory, with the minimum of technical requirements. Special properties of subordinators are developed and then appear as key features in the study of the local times of real-valued Lévy processes and in fluctuation theory. Lévy processes with no positive jumps receive special attention, as do stable processes. In sum, this will become the standard reference on the subject for all working probability theorists.
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Editorial Reviews
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"I think this is THE book on the subject, rather than A book on it. The text is clearly written, and very well organised. The subject-matter is mainstream probability, so will always be topical. A book on these lines has been long overdue..." Professor Nick Bingham
"This concise book promises to be the standard reference for students and researchers concerned with this field." Monatshefte fur Mathematik
"This concise book promises to be the standard reference for students and researchers concerned with this field." Monatshefte fur Mathematik
Book Description
This is an up-to-date and comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin uses the interplay between the probabilistic structure and analytic tools to give a quick and concise treatment of the core theory, with the minimum of technical requirements. This will become the standard reference on the subject for all working probability theorists.'I think this is THE book on the subject, rather than A book on it. The text is clearly written, and very well organised. The subject-matter is mainstream probability, so will always be topical. A book on these lines has been long overdue.' Professor Nick Bingham
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Inside This Book
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First Sentence:
In this section, we set down notation which will be used throughout the text. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
ladder time set, generalized arcsine law, isotropic stable process, last passage time, generic excursion, ladder height process, inverse local time, excursion intervals, normalized excursion, independent exponential time, positive continuous additive functional, excursion measure, continuous local times, occupation density formula, positivity parameter, supremum process, sample path behaviour, excursion theory, excursion process, first entrance time, arcsine laws, stable subordinator, positive jumps, fluctuation identities, symmetric stable processes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Sparre Andersen, Applying Proposition, Proof First, Proof Fix New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this section, we set down notation which will be used throughout the text. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
ladder time set, generalized arcsine law, isotropic stable process, last passage time, generic excursion, ladder height process, inverse local time, excursion intervals, normalized excursion, independent exponential time, positive continuous additive functional, excursion measure, continuous local times, occupation density formula, positivity parameter, supremum process, sample path behaviour, excursion theory, excursion process, first entrance time, arcsine laws, stable subordinator, positive jumps, fluctuation identities, symmetric stable processes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Sparre Andersen, Applying Proposition, Proof First, Proof Fix New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
2
books
cite this book:
- Probability and Finance: It's Only a Game! by Glenn Shafer in Back Matter
- Equity Derivatives: Theory and Applications by Marcus Overhaus in Back Matter
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