Overview
- The first and so far the only book in this area
- Presents the important results in a coherent and unified manner
- Includes systematic, creative and original ways to use sophisticated (but highly technical) tools
- Includes supplementary material: sn.pub/extras
Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 67)
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Table of contents (16 chapters)
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Front Matter
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Introduction and Preliminary Material
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Front Matter
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More Laws of Large Numbers
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Front Matter
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Extensions of the Central Limit Theorems
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Front Matter
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Various Extensions
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Front Matter
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Keywords
- 60F05, 60G44, 60H10, 60H35, 60J75, 60G51, 60G57
- asymptotic error
- central limit theorem for stochastic processes
- density forecasting
- estimation
- jump processes
- law of large numbers for stochastic processes
- semimartingale
- stable convergence
- stochastic processes
- time-varying correlation
- volatility
- weak convergence
- white noise
About this book
In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, “In God we trust; all others must bring data.”
This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings.
This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics.
Reviews
From the reviews:
“It is clearly statistically oriented and intended to help practitioners to answer questions about an observed random process X. … The book may be considered as the outcome of several decades of intensive work on the statistics of semimartingales, and a large part of the stated results is due to the authors. For both theoreticians and practitioners in the vast realm of random processes, this will be an indispensable reference book.” (Dominique Lépingle, Mathematical Reviews, January, 2013)
“This new book develops a theory of limit theorems for discretely observed Itô semimartingales with a view towards statistical applications. … This monograph by two leading experts in the field of stochastic processes will certainly become a standard reference when statistical questions in semimartingale models need to be investigated. The text is very well written and is without doubt a must have for scientists interested in applications of advanced stochastic process models.” (H. M. Mai, Zentralblatt MATH, Vol. 1259, 2013)
Authors and Affiliations
Bibliographic Information
Book Title: Discretization of Processes
Authors: Jean Jacod, Philip Protter
Series Title: Stochastic Modelling and Applied Probability
DOI: https://doi.org/10.1007/978-3-642-24127-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Hardcover ISBN: 978-3-642-24126-0Published: 23 October 2011
Softcover ISBN: 978-3-642-26950-9Published: 28 November 2013
eBook ISBN: 978-3-642-24127-7Published: 22 October 2011
Series ISSN: 0172-4568
Series E-ISSN: 2197-439X
Edition Number: 1
Number of Pages: XVI, 596
Topics: Probability Theory and Stochastic Processes, Statistics for Business, Management, Economics, Finance, Insurance, Econometrics