Fundamentals Of The Theory Of Structured Dependence Between Stochastic Processes
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Fundamentals of the Theory of Structured Dependence between Stochastic Processes
Author: Tomasz R. Bielecki
language: en
Publisher: Cambridge University Press
Release Date: 2020-08-27
Comprehensive presentation of the technical aspects and applications of the theory of structured dependence between random processes.
Foundations of Constructive Probability Theory
Author: Yuen-Kwok Chan
language: en
Publisher: Cambridge University Press
Release Date: 2021-05-27
This book provides a systematic and general theory of probability within the framework of constructive mathematics.
Discretization of Processes
Author: Jean Jacod
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-10-22
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.