Discretization of processes
 Author/Creator
 Jacod, Jean.
 Language
 English.
 Imprint
 Heidelberg ; New York : SpringerVerlag Berlin Heidelberg, c2012.
 Physical description
 xiv, 596 p. : ill. ; 24 cm.
 Series
 Stochastic modelling and applied probability 67.
Access
Contributors
 Contributor
 Protter, Philip E.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Part I Introduction and Preliminary Material. 1.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. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 In applications, and especially in mathematical finance, random timedependent 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Stochastic analysis.
Bibliographic information
 Publication date
 2012
 Responsibility
 Jean Jacod, Philip Protter.
 Series
 Stochastic modelling and applied probability, 01724568 ; 67.
 ISBN
 9783642241260
 3642241263