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Discretization of Processes

2011-10-22 Mathematics
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Release : 2011-10-22
Genre : Mathematics
Kind : eBook
Book Rating : 271/5 ( reviews)

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Book Synopsis Discretization of Processes by : Jean Jacod

Download or read book Discretization of Processes written by Jean Jacod. This book was released on 2011-10-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discretization Methods in Structural Mechanics

2013-03-08 Technology & Engineering
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Release : 2013-03-08
Genre : Technology & Engineering
Kind : eBook
Book Rating : 734/5 ( reviews)

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Book Synopsis Discretization Methods in Structural Mechanics by : Günther Kuhn

Download or read book Discretization Methods in Structural Mechanics written by Günther Kuhn. This book was released on 2013-03-08. Available in PDF, EPUB and Kindle. Book excerpt: The advent of the digital computer has given great impetus to the development of modern discretization methods in structural mechanics. The young history of the finite element method (FEM) reflects the dramatic increase of computing speed and storage capacity within a relatively short period of time. The history of the boundary element method (BEM) is still younger. Presently, intense scientific efforts aimed at extending the range of application of the BEM can be observed. More than 10 years ago, O.C. Zienkiewicz and his co-workers published the first papers on the coupling of FE and BE discretizations of subregions of solids for the purpose of exploiting the complementary advantages of the two discretization methods and reducing their disadvantages. The FEM has revolutionized structural analysis in industry as well as academia. The BEM has a fair share in the continuation of this revolution. Both discretization methods have become a domain of vigorous, world-wide research activities. The rapid increase of the number of specialized journals and scientific meetings indicates the remarkable increase of research efforts in this important subdolll.ain of computational ulechanics. Several discussions of this situation in the Committee for Discretization Methods ill Solid Mechanics of the Society for Applied Mathematics and Mechanics (GAMM) resulted in the plan to submit a proposal to the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM) to sponsor a pertinent IUTAM Symposium.

On asymptotic errors in discretization of processes

2001
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Release : 2001
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis On asymptotic errors in discretization of processes by : J. Jacod

Download or read book On asymptotic errors in discretization of processes written by J. Jacod. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt:

Discrete Stochastic Processes

2012-12-06 Technology & Engineering
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Release : 2012-12-06
Genre : Technology & Engineering
Kind : eBook
Book Rating : 29X/5 ( reviews)

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Book Synopsis Discrete Stochastic Processes by : Robert G. Gallager

Download or read book Discrete Stochastic Processes written by Robert G. Gallager. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.

Analysis of Discretization Methods for Ordinary Differential Equations

2013-03-12 Mathematics
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Release : 2013-03-12
Genre : Mathematics
Kind : eBook
Book Rating : 711/5 ( reviews)

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Book Synopsis Analysis of Discretization Methods for Ordinary Differential Equations by : Hans J. Stetter

Download or read book Analysis of Discretization Methods for Ordinary Differential Equations written by Hans J. Stetter. This book was released on 2013-03-12. Available in PDF, EPUB and Kindle. Book excerpt: Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential equation problem, usually by a projection into a finite-dimensional space. By far the most popular of these finitization processes consists of a reduction to a difference equation problem for functions which take values only on a grid of argument points. Although some of these finite difference methods have been known for a long time, their wide applica bility and great efficiency came to light only with the spread of electronic computers. This in tum strongly stimulated research on the properties and practical use of finite-difference methods. While the theory or partial differential equations and their discrete analogues is a very hard subject, and progress is consequently slow, the initial value problem for a system of first order ordinary differential equations lends itself so naturally to discretization that hundreds of numerical analysts have felt inspired to invent an ever-increasing number of finite-difference methods for its solution. For about 15 years, there has hardly been an issue of a numerical journal without new results of this kind; but clearly the vast majority of these methods have just been variations of a few basic themes. In this situation, the classical text book by P.

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