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Titlebook: Discretization of Processes; Jean Jacod,Philip Protter Book 2012 Springer-Verlag Berlin Heidelberg 2012 60F05, 60G44, 60H10, 60H35, 60J75,

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书目名称Discretization of Processes
编辑Jean Jacod,Philip Protter
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概述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 technic
丛书名称Stochastic Modelling and Applied Probability
图书封面Titlebook: Discretization of Processes;  Jean Jacod,Philip Protter Book 2012 Springer-Verlag Berlin Heidelberg 2012 60F05, 60G44, 60H10, 60H35, 60J75,
描述.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 biolo
出版日期Book 2012
关键词60F05, 60G44, 60H10, 60H35, 60J75, 60G51, 60G57; asymptotic error; central limit theorem for stochasti
版次1
doihttps://doi.org/10.1007/978-3-642-24127-7
isbn_softcover978-3-642-26950-9
isbn_ebook978-3-642-24127-7Series ISSN 0172-4568 Series E-ISSN 2197-439X
issn_series 0172-4568
copyrightSpringer-Verlag Berlin Heidelberg 2012
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0172-4568 nterest 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 biolo978-3-642-26950-9978-3-642-24127-7Series ISSN 0172-4568 Series E-ISSN 2197-439X
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https://doi.org/10.1007/978-3-319-50219-9hem here..Section 2.2 is devoted to recalling facts about the convergence of processes, starting with a quick reminder about the Skorokhod topology. Here, special emphasis is put on ., which is central for almost all statistical applications of the results of this book. Again, the proofs of most res
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Laws of Large Numbers: The Basic Resultson scheme goes to 0..In contrast, the Law of Large Numbers for the normalized functionals .′.(.,.), in which the argument of the test function . is taken to be the increment of . on each discretization interval, divided by the square-root of its length, holds only for Itô semimartingales and for reg
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Central Limit Theorems: Technical Toolsted to a description of the limiting processes occurring in the various Central Limit Theorems, and which are processes with “conditionally independent increments”. Sections 4.2 and 4.3 provide general criteria for stable convergence in law, when the limit is a continuous process (Sect. 4.3) or a po
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