Stochastic Modelling and Applied Probability

Discretization of Processes

Authors: Jacod, Jean, Protter, Philip E.

  • 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 
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eBook $99.00
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  • ISBN 978-3-642-24127-7
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  • Immediate eBook download after purchase
Hardcover $129.00
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  • ISBN 978-3-642-24126-0
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Softcover $129.00
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  • ISBN 978-3-642-26950-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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)


Table of contents (16 chapters)

  • Introduction

    Jacod, Jean (et al.)

    Pages 3-21

  • Some Prerequisites

    Jacod, Jean (et al.)

    Pages 23-59

  • Laws of Large Numbers: The Basic Results

    Jacod, Jean (et al.)

    Pages 63-96

  • Central Limit Theorems: Technical Tools

    Jacod, Jean (et al.)

    Pages 97-123

  • Central Limit Theorems: The Basic Results

    Jacod, Jean (et al.)

    Pages 125-185

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-24127-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-24126-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-642-26950-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Discretization of Processes
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
67
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-24127-7
DOI
10.1007/978-3-642-24127-7
Hardcover ISBN
978-3-642-24126-0
Softcover ISBN
978-3-642-26950-9
Series ISSN
0172-4568
Edition Number
1
Number of Pages
XVI, 596
Topics