Stochastics

The increase in the requirements on the reliability of units makes it necessary to analyze the relationship between mathematicalmeth- ods of calculating reliability and the physical nature of fail- ures.

In Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R.

It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe- matical discipline.

This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the explanation of large-scale dynamics (evolution differential equations) from models of a very large number of interacting particles.

These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974.

The NATO Advanced Study Institute From Statistics to Neural Networks, Theory and Pattern Recognition Applications took place in Les Arcs, Bourg Saint Maurice, France, from June 21 through July 2, 1993.

The favourable reception of the first edition and the encouragement received from many readers have prompted the author to bring out this new edition.

One-dimensional dynamics has developed in the last decades into a subject in its own right.

The purpose of this book is to give a streamlined introduction to the theory of (not necessarily symmetric) Dirichlet forms on general state spaces.

Our life is a highly nonlinear process.

The primary aim of this monograph is to provide a formal framework for the representation and management of uncertainty and vagueness in the field of artificial intelligence.

Adaptive systems are widely encountered in many applications ranging through adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, to pattern recognition and machine intelligence: adaptation is now recognised as keystone of "e;intelligence"e; within computerised systems.

Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic calculus.

This book presents a comprehensive collection of integrals of the Fourier transformation type.

The second edition has not deviated significantly from the first.

Today, the theory of random processes represents a large field of mathematics with many different branches, and the task of choosing topics for a brief introduction to this theory is far from being simple.

This version differs from the Portuguese edition only in a few additions and many minor corrections.

Markov processes play an important role in the study of probability theory.

This book contains the invited papers of the interdisciplinary workshop on "e;Stochastic Nonlinear Systems in Physics, Chemistry and Biology"e; held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980.

The objective of the present edition of this monograph is the same as that of earlier editions, namely, to provide readers with some mathemati- cal maturity a rigorous and modern introduction to the ideas and principal theorems of probabilistic information theory.

In anglo-american literature there exist numerous books, devoted to the application of the Laplace transformation in technical domains such as electrotechnics, mechanics etc.

In this book problems related to the choice of models in such diverse fields as regression, covariance structure, time series analysis and multinomial experiments are discussed.

The orthogonality of functions has been exploited in communications since its very beginning.

Project planning, scheduling, and control are regularly used in business and the service sector of an economy to accomplish outcomes with limited resources under critical time constraints.

Searching is an important process in most AI systems, especially in those AI production systems consisting of a global database, a set of production rules, and a control system.

DYNAMICS REPORTED reports on recent developments in dynamical systems.

I have been pleased with the favourable reception of the first edition of this book and I am grateful to have the opportunity to prepare this second edition.

A volume of this nature containing a collection of papers has been brought out to honour a gentleman - a friend and a colleague - whose work has, to a large extent, advanced and popularized the use of stochastic point processes.

Over the last fifty years advanced mathematical tools have become an integral part in the development of modern economic theory.

C-XSC is a tool for the development of numerical algorithms delivering highly accurate and automatically verified results.

The numerical solution of stochastic differential equations is becoming an in- dispensible worktool in a multitude of disciplines, bridging a long-standing gap between the well advanced theory of stochastic differential equations and its application to specific examples.

This monograph contains: - ten papers written by the author, and co-authors, between December 1988 and October 1998 about certain exponential functionals of Brownian motion and related processes, which have been, and still are, of interest, during at least the last decade, to researchers in Mathematical finance; - an introduction to the subject from the view point of Mathematical Finance by H.

The Galton-Watson branching process has its roots in the problem of extinction of family names which was given a precise formulation by F.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.