Discretization of Processes
(Sprache: Englisch)
Using classic statistical tools, this book synthesizes ten years of research to establish a sohisticated theory of how to go about estimating not just scalar parameters of a proposed model, but also the underlying structure of the model itself.
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Produktinformationen zu „Discretization of Processes “
Using classic statistical tools, this book synthesizes ten years of research to establish a sohisticated theory of how to go about estimating not just scalar parameters of a proposed model, but also the underlying structure of the model itself.
Klappentext zu „Discretization of Processes “
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.
Inhaltsverzeichnis zu „Discretization of Processes “
Part I Introduction and Preliminary Material1.Introduction
2.Some Prerequisites
Part II The Basic Results
3.Laws of Large Numbers: the Basic Results
4.Central Limit Theorems: Technical Tools
5.Central Limit Theorems: the Basic Results
6.Integrated Discretization Error
Part III More Laws of Large Numbers
7.First Extension: Random Weights
8.Second Extension: Functions of Several Increments
9.Third Extension: Truncated Functionals
Part IV Extensions of the Central Limit Theorems
10.The Central Limit Theorem for Random Weights
11.The Central Limit Theorem for Functions of a Finite Number of Increments
12.The Central Limit Theorem for Functions of an Increasing Number of Increments
13.The Central Limit Theorem for Truncated Functionals
Part V Various Extensions
14.Irregular Discretization Schemes
15.Higher Order Limit Theorems
16.Semimartingales Contaminated by Noise
- Appendix
- References
- Assumptions
- Index of Functionals
- Indexic Results
3.Laws of Large Numbers: the Basic Results
4.Central Limit Theorems: Technical Tools
5.Central Limit Theorems: the Basic Results
6.Integrated Discretization Error
Part III More Laws of Large Numbers
7.First Extension: Random Weights
8.Second Extension: Functions of Several Increments
9.Third Extension: Truncated Functionals
Part IV Extensions of the Central Limit Theorems
10.The Central Limit Theorem for Random Weights
11.The Central Limit Theorem for Functions of a Finite Number of Increments
12.The Central Limit Theorem for Functions of an Increasing Number of Increments
13.The Central Limit Theorem for Truncated Functionals
Part V Various Extensions
14.Irregular Discretization Schemes
15.Higher Order Limit Theorems
16.Semimartingales Contamina
Bibliographische Angaben
- Autoren: Jean Jacod , Philip E. Protter
- 2011, 2012, XVI, 596 Seiten, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642241263
- ISBN-13: 9783642241260
- Erscheinungsdatum: 23.10.2011
Sprache:
Englisch
Rezension zu „Discretization of Processes “
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)
Pressezitat
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)
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