A Road To Randomness In Physical Systems
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A Road To Randomness In Physical Systems
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Author : Eduardo M R a Engel
language : en
Publisher:
Release Date : 1992-02-01
A Road To Randomness In Physical Systems written by Eduardo M R a Engel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-01 with categories.
A Road To Randomness In Physical Systems
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Author : Eduardo M.R.A. Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Road To Randomness In Physical Systems written by Eduardo M.R.A. Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
There are many ways of introducing the concept of probability in classical, i. e, deter ministic, physics. This work is concerned with one approach, known as "the method of arbitrary funetionJ. " It was put forward by Poincare in 1896 and developed by Hopf in the 1930's. The idea is the following. There is always some uncertainty in our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. A probability density may be used to describe this uncertainty. For many physical systems, dependence on the initial density washes away with time. Inthese cases, the system's position eventually converges to the same random variable, no matter what density is used to describe initial uncertainty. Hopf's results for the method of arbitrary functions are derived and extended in a unified fashion in these lecture notes. They include his work on dissipative systems subject to weak frictional forces. Most prominent among the problems he considers is his carnival wheel example, which is the first case where a probability distribution cannot be guessed from symmetry or other plausibility considerations, but has to be derived combining the actual physics with the method of arbitrary functions. Examples due to other authors, such as Poincare's law of small planets, Borel's billiards problem and Keller's coin tossing analysis are also studied using this framework. Finally, many new applications are presented.
Random Sums And Branching Stochastic Processes
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Author : Ibrahim Rahimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Sums And Branching Stochastic Processes written by Ibrahim Rahimov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
Stochastic Visibility In Random Fields
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Author : Shelemyahu Zacks
language : en
Publisher: Springer
Release Date : 2012-12-06
Stochastic Visibility In Random Fields written by Shelemyahu Zacks and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present monograph is a comprehensive summary of the research on visibility in random fields, which I have conducted with the late Professor Micha Yadin for over ten years. This research, which resulted in several published papers and technical reports (see bibliography), was motivated by some military problems, which were brought to our attention by Mr. Pete Shugart of the US Army TRADOC Systems Analysis Activity, presently called US Army TRADOC Analysis Command. The Director ofTRASANA at the time, the late Dr. Wilbur Payne, identified the problems and encouraged the support and funding of this research by the US Army. Research contracts were first administered through the Office of Naval Research, and subsequently by the Army Research Office. We are most grateful to all involved for this support and encouragement. In 1986 I administered a three-day workshop on problem solving in the area of sto chastic visibility. This workshop was held at the White Sands Missile Range facility. A set of notes with some software were written for this workshop. This workshop led to the incorporation of some of the methods discussed in the present book into the Army simulation package CASTFOREM. Several people encouraged me to extend those notes and write the present monograph on the level of those notes, so that the material will be more widely available for applications.
Ten Great Ideas About Chance
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Author : Persi Diaconis
language : en
Publisher: Princeton University Press
Release Date : 2019-10-08
Ten Great Ideas About Chance written by Persi Diaconis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.
In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.
Causation Physics And The Constitution Of Reality
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Author : Huw Price
language : en
Publisher:
Release Date : 2007
Causation Physics And The Constitution Of Reality written by Huw Price and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Philosophy categories.
The difference between cause and effect seems obvious and crucial in ordinary life, yet missing from modern physics. Almost a century ago, Bertrand Russell called the law of causality "a relic of a bygone age". In this important collection 13 leading scholars revisit Russell's revolutionary conclusion, discussing one of the most significant and puzzling issues in contemporary thought.
Dirichlet Forms Methods For Poisson Point Measures And L Vy Processes
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Author : Nicolas Bouleau
language : en
Publisher: Springer
Release Date : 2016-01-08
Dirichlet Forms Methods For Poisson Point Measures And L Vy Processes written by Nicolas Bouleau and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-08 with Mathematics categories.
A simplified approach to Malliavin calculus adapted to Poisson random measures is developed and applied in this book. Called the “lent particle method” it is based on perturbation of the position of particles. Poisson random measures describe phenomena involving random jumps (for instance in mathematical finance) or the random distribution of particles (as in statistical physics). Thanks to the theory of Dirichlet forms, the authors develop a mathematical tool for a quite general class of random Poisson measures and significantly simplify computations of Malliavin matrices of Poisson functionals. The method gives rise to a new explicit calculus that they illustrate on various examples: it consists in adding a particle and then removing it after computing the gradient. Using this method, one can establish absolute continuity of Poisson functionals such as Lévy areas, solutions of SDEs driven by Poisson measure and, by iteration, obtain regularity of laws. The authors also give applications to error calculus theory. This book will be of interest to researchers and graduate students in the fields of stochastic analysis and finance, and in the domain of statistical physics. Professors preparing courses on these topics will also find it useful. The prerequisite is a knowledge of probability theory.
Learning From Data
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Author : Doug Fisher
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Learning From Data written by Doug Fisher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Ten years ago Bill Gale of AT&T Bell Laboratories was primary organizer of the first Workshop on Artificial Intelligence and Statistics. In the early days of the Workshop series it seemed clear that researchers in AI and statistics had common interests, though with different emphases, goals, and vocabularies. In learning and model selection, for example, a historical goal of AI to build autonomous agents probably contributed to a focus on parameter-free learning systems, which relied little on an external analyst's assumptions about the data. This seemed at odds with statistical strategy, which stemmed from a view that model selection methods were tools to augment, not replace, the abilities of a human analyst. Thus, statisticians have traditionally spent considerably more time exploiting prior information of the environment to model data and exploratory data analysis methods tailored to their assumptions. In statistics, special emphasis is placed on model checking, making extensive use of residual analysis, because all models are 'wrong', but some are better than others. It is increasingly recognized that AI researchers and/or AI programs can exploit the same kind of statistical strategies to good effect. Often AI researchers and statisticians emphasized different aspects of what in retrospect we might now regard as the same overriding tasks.
Nonparametric Statistics For Stochastic Processes
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Author : Denis Bosq
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonparametric Statistics For Stochastic Processes written by Denis Bosq and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.
Graphical Methods For The Design Of Experiments
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Author : Russell R. Barton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Graphical Methods For The Design Of Experiments written by Russell R. Barton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Graphical methods have played an important role in the statistical analysis of experimental data, but have not been used as extensively for experiment design, at least as it is presented in most design of experiments texts. Yet graphical methods are particularly attractive for the design of experiments because they exploit our creative right-brain capabilities. Creative activity is clearly important in any kind of design, certainly for the design ofan experiment. The experimenter must somehow select a set of run conditions that will meet the goals for a particular experiment in a cost-efficient way. Graphical Methods for Experiment Design goes beyond graphical methods for choosing run conditions for an experiment. It looks at the entire pre-experiment planning process, and presents in one place a collection of graphical methods for defining experiment goals, identifying and classifying variables, for choosing a model, for developing a design, and for assessing the adequacy of a design for estimating the unknown coefficients in the proposed statistical model. In addition, tools for developing a design also provide a platform for viewing the results of the experiment, a platform that provides insights that cannot be obtained by examination ofregression coefficients. These techniques can be applied to a variety of situations, including experimental runs of computer simulation models. Factorial and fractional-factorial designs are the focus of the graphical representations, although mixture experiments and experiments involving random effects and blocking are designed and represented in similar ways.