Discretization Of Processes
Download Discretization Of Processes PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Discretization Of Processes book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
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.
Process Algebra with Timing
Author: J.C.M. Baeten
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
This book is concerned with a number of theories that can be used for describ ing and analyzing systems of interacting components in case it is desirable or necessary to regard their time-dependent behavior. Society is becoming increasingly more dependent on complex computer based systems that are composed of several components that act concurrently and interact - to synchronize and communicate with each other. The com plexity of these systems arises to a great extent from the many ways in which their components can interact. The need that these components act and in teract on time as well adds considerably to the complexity. In developing such a system, it is important to be able to acquire a better understanding of the relevant issues at the conceptual level, to describe the system in a precise way at various levels of detail, and to analyze it on the basis of the descriptions. When the early algebraic theories about processes, such as ACP [16, 17, 20], CCS [49, 50] and CSP [27, 39], were developed for that purpose, the established opinion was still that timing is a concern that can more often than not be treated independently. It is therefore not surprising that timing is deliberately ignored in those theories. They have now all been extended to deal with timing.
Controlled Stochastic Processes
Author: I. I. Gihman
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The theory of controlled processes is one of the most recent mathematical theories to show very important applications in modern engineering, parti cularly for constructing automatic control systems, as well as for problems of economic control. However, actual systems subject to control do not admit a strictly deterministic analysis in view of random factors of various kinds which influence their behavior. Such factors include, for example, random noise occurring in the electrical system, variations in the supply and demand of commodities, fluctuations in the labor force in economics, and random failures of components on an automated line. The theory of con trolled processes takes the random nature of the behavior of a system into account. In such cases it is natural, when choosing a control strategy, to proceed from the average expected result, taking note of all the possible variants of the behavior of a controlled system. An extensive literature is devoted to various economic and engineering systems of control (some of these works are listed in the Bibliography). is no text which adequately covers the general However, as of now there mathematical theory of controlled processes. The authors ofthis monograph have attempted to fill this gap. In this volume the general theory of discrete-parameter (time) controlled processes (Chapter 1) and those with continuous-time (Chapter 2), as well as the theory of controlled stochastic differential equations (Chapter 3), are presented.