Randomness And Hyper Randomness PDF Download
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| Author | : Igor I. Gorban |
| Publisher | : Springer |
| Total Pages | : 240 |
| Release | : 2017-08-31 |
| Genre | : Technology & Engineering |
| ISBN | : 3319607804 |
Download Randomness and Hyper-randomness Book in PDF, ePub and Kindle
The monograph compares two approaches that describe the statistical stability phenomenon – one proposed by the probability theory that ignores violations of statistical stability and another proposed by the theory of hyper-random phenomena that takes these violations into account. There are five parts. The first describes the phenomenon of statistical stability. The second outlines the mathematical foundations of probability theory. The third develops methods for detecting violations of statistical stability and presents the results of experimental research on actual processes of different physical nature that demonstrate the violations of statistical stability over broad observation intervals. The fourth part outlines the mathematical foundations of the theory of hyper-random phenomena. The fifth part discusses the problem of how to provide an adequate description of the world. The monograph should be interest to a wide readership: from university students on a first course majoring in physics, engineering, and mathematics to engineers, post-graduate students, and scientists carrying out research on the statistical laws of natural physical phenomena, developing and using statistical methods for high-precision measurement, prediction, and signal processing over broad observation intervals. To read the book, it is sufficient to be familiar with a standard first university course on mathematics.
| Author | : M. Rosenblatt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 236 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461298520 |
Download Random Processes Book in PDF, ePub and Kindle
This text has as its object an introduction to elements of the theory of random processes. Strictly speaking, only a good background in the topics usually associated with a course in Advanced Calculus (see, for example, the text of Apostol [1]) and the elements of matrix algebra is required although additional background is always helpful. N onethe less a strong effort has been made to keep the required background on the level specified above. This means that a course based on this book would be appropriate for a beginning graduate student or an advanced undergraduate. Previous knowledge of probability theory is not required since the discussion starts with the basic notions of probability theory. Chapters II and III are concerned with discrete probability spaces and elements of the theory of Markov chains respectively. These two chapters thus deal with probability theory for finite or countable models. The object is to present some of the basic ideas and problems of the theory in a discrete context where difficulties of heavy technique and detailed measure theoretic discussions do not obscure the ideas and problems.
| Author | : Edward Beltrami |
| Publisher | : Springer Nature |
| Total Pages | : 192 |
| Release | : 2020-07-30 |
| Genre | : Mathematics |
| ISBN | : 1071607995 |
Download What Is Random? Book in PDF, ePub and Kindle
In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive, but Godels undecidability theorem informs us that we will never know. Those familiar with quantum indeterminacy assert that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Perhaps order and randomness, like waves and particles, are only two sides of the same (tossed) coin.
| Author | : Syski |
| Publisher | : CRC Press |
| Total Pages | : 444 |
| Release | : 2020-10-28 |
| Genre | : Mathematics |
| ISBN | : 1000103870 |
Download Random Processes Book in PDF, ePub and Kindle
This book develops appreciation of the ingenuity involved in the mathematical treatment of random phenomena, and of the power of the mathematical methods employed in the solution of applied problems. It is intended to students interested in applications of probability to their disciplines.
| Author | : Ilya Molchanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 508 |
| Release | : 2005-05-11 |
| Genre | : Mathematics |
| ISBN | : 9781852338923 |
Download Theory of Random Sets Book in PDF, ePub and Kindle
This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
| Author | : Igor N. Kovalenko |
| Publisher | : CRC Press |
| Total Pages | : 456 |
| Release | : 1996-07-08 |
| Genre | : Mathematics |
| ISBN | : 9780849328701 |
Download Models of Random Processes Book in PDF, ePub and Kindle
Devising and investigating random processes that describe mathematical models of phenomena is a major aspect of probability theory applications. Stochastic methods have penetrated into an unimaginably wide scope of problems encountered by researchers who need stochastic methods to solve problems and further their studies. This handbook supplies the knowledge you need on the modern theory of random processes. Packed with methods, Models of Random Processes: A Handbook for Mathematicians and Engineers presents definitions and properties on such widespread processes as Poisson, Markov, semi-Markov, Gaussian, and branching processes, and on special processes such as cluster, self-exiting, double stochastic Poisson, Gauss-Poisson, and extremal processes occurring in a variety of different practical problems. The handbook is based on an axiomatic definition of probability space, with strict definitions and constructions of random processes. Emphasis is placed on the constructive definition of each class of random processes, so that a process is explicitly defined by a sequence of independent random variables and can easily be implemented into the modelling. Models of Random Processes: A Handbook for Mathematicians and Engineers will be useful to researchers, engineers, postgraduate students and teachers in the fields of mathematics, physics, engineering, operations research, system analysis, econometrics, and many others.
| Author | : Yurii A. Rozanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 127 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642727174 |
Download Introduction to Random Processes Book in PDF, ePub and Kindle
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 introduction to the theory of random processes uses mathematical models that are simple, but have some importance for applications. We consider different processes, whose development in time depends on some random factors. The fundamental problem can be briefly circumscribed in the following way: given some relatively simple characteristics of a process, compute the probability of another event which may be very complicated; or estimate a random variable which is related to the behaviour of the process. The models that we consider are chosen in such a way that it is possible to discuss the different methods of the theory of random processes by referring to these models. The book starts with a treatment of homogeneous Markov processes with a countable number of states. The main topic is the ergodic theorem, the method of Kolmogorov's differential equations (Secs. 1-4) and the Brownian motion process, the connecting link being the transition from Kolmogorov's differential-difference equations for random walk to a limit diffusion equation (Sec. 5).
| Author | : Oliver Ibe |
| Publisher | : Academic Press |
| Total Pages | : 457 |
| Release | : 2014-06-13 |
| Genre | : Mathematics |
| ISBN | : 0128010355 |
Download Fundamentals of Applied Probability and Random Processes Book in PDF, ePub and Kindle
The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. Demonstrates concepts with more than 100 illustrations, including 2 dozen new drawings Expands readers’ understanding of disruptive statistics in a new chapter (chapter 8) Provides new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts. Includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9).
| Author | : Stanford University. Stanford Electronics Laboratories. Information Systems Laboratory |
| Publisher | : |
| Total Pages | : 204 |
| Release | : 1995 |
| Genre | : |
| ISBN | : |
Download Random Processes Book in PDF, ePub and Kindle
| Author | : Eduardo M.R.A. Engel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 166 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1441986847 |
Download A Road to Randomness in Physical Systems Book in PDF, ePub and Kindle
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.
