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Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Damiano Rossello
Publisher: Springer Nature
ISBN: 3031546881
Category :
Languages : en
Pages : 401
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Book Description
Author: Robert M. Gray
Publisher: Springer Science & Business Media
ISBN: 1441910905
Category : Technology & Engineering
Languages : en
Pages : 348
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Book Description
Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing. It will also interest those working with random or stochastic processes, including mathematicians, statisticians, and economists. Highlights: Complete tour of book and guidelines for use given in Introduction, so readers can see at a glance the topics of interest. Structures mathematics for an engineering audience, with emphasis on engineering applications. New in the Second Edition: Much of the material has been rearranged and revised for pedagogical reasons. The original first chapter has been split in order to allow a more thorough treatment of basic probability before tackling random processes and dynamical systems. The final chapter has been broken into two pieces to provide separate emphasis on process metrics and the ergodic decomposition of affine functionals. Many classic inequalities are now incorporated into the text, along with proofs; and many citations have been added.
Author: Evarist Giné
Publisher: Springer Science & Business Media
ISBN: 1461213584
Category : Mathematics
Languages : en
Pages : 491
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Book Description
High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.
Author: Kai Lai Chung
Publisher: Academic Press
ISBN: 0080570402
Category : Mathematics
Languages : en
Pages : 381
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Book Description
This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.
Author: Hisashi Kobayashi
Publisher: Cambridge University Press
ISBN: 1139502611
Category : Technology & Engineering
Languages : en
Pages : 813
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Book Description
Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.
Author: Bľa Bollobs̀ (ed)
Publisher: American Mathematical Soc.
ISBN: 082185500X
Category : Mathematics
Languages : en
Pages : 214
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Book Description
Probabilistic methods have become a vital tool in the arsenal of every combinatorialist. The theory of random graphs is still a prime area for the use of probabilistic methods, and, over the years, these methods have also proved of paramount importance in many associated areas such as the design and analysis of computer algorithms. In recent years, probabilistic combinatorics has undergone revolutionary changes as the result of the appearance of some exciting new techniques such as martingale inequalities, discrete isoperimetric inequalities, Fourier analysis on groups, eigenvalue techniques, branching processes, and rapidly mixing Markov chains. The aim of this volume is to review briefly the classical results in the theory of random graphs and to present several of the important recent developments in probabilistic combinatorics, together with some applications. The first paper contains a brief introduction to the theory of random graphs. The second paper reviews explicit constructions of random-like graphs and discusses graphs having a variety of useful properties. Isoperimetric inequalities, of paramount importance in probabilistic combinatorics, are covered in the third paper. The chromatic number of random graphs is presented in the fourth paper, together with a beautiful inequality due to Janson and the important and powerful Stein-Chen method for Poisson approximation. The aim of the fifth paper is to present a number of powerful new methods for proving that a Markov chain is "rapidly mixing" and to survey various related questions, while the sixth paper looks at the same topic in a very different context. For the random walk on the cube, the convergence to the stable distribution is best analysed through Fourier analysis; the final paper examines this topic and proceeds to several more sophisticated applications. Open problems can be found throughout each paper.
Author: Marc A. Berger
Publisher: Springer Science & Business Media
ISBN: 1461227267
Category : Mathematics
Languages : en
Pages : 228
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Book Description
These notes were written as a result of my having taught a "nonmeasure theoretic" course in probability and stochastic processes a few times at the Weizmann Institute in Israel. I have tried to follow two principles. The first is to prove things "probabilistically" whenever possible without recourse to other branches of mathematics and in a notation that is as "probabilistic" as possible. Thus, for example, the asymptotics of pn for large n, where P is a stochastic matrix, is developed in Section V by using passage probabilities and hitting times rather than, say, pulling in Perron Frobenius theory or spectral analysis. Similarly in Section II the joint normal distribution is studied through conditional expectation rather than quadratic forms. The second principle I have tried to follow is to only prove results in their simple forms and to try to eliminate any minor technical com putations from proofs, so as to expose the most important steps. Steps in proofs or derivations that involve algebra or basic calculus are not shown; only steps involving, say, the use of independence or a dominated convergence argument or an assumptjon in a theorem are displayed. For example, in proving inversion formulas for characteristic functions I omit steps involving evaluation of basic trigonometric integrals and display details only where use is made of Fubini's Theorem or the Dominated Convergence Theorem.
Author: Mor Harchol-Balter
Publisher: Cambridge University Press
ISBN: 1009309072
Category : Computers
Languages : en
Pages : 573
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Book Description
A highly engaging and interactive undergraduate textbook specifically written for computer science courses.
Author: Steven J. Miller
Publisher: Princeton University Press
ISBN: 0691149550
Category : Mathematics
Languages : en
Pages : 752
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Book Description
The essential lifesaver for students who want to master probability For students learning probability, its numerous applications, techniques, and methods can seem intimidating and overwhelming. That's where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly study guide helps students comfortably navigate probability's terrain and achieve positive results. The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement—both in the guide and on the book's website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus. The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses. A helpful introduction to probability or a perfect supplement for a course Numerous worked-out examples Lectures based on the chapters are available free online Intuition of problems emphasized first, then technical proofs given Appendixes review proof techniques Relaxed, conversational approach
