How to Gamble If You Must

Author: Lester E. Dubins
Publisher: Courier Corporation
ISBN: 9780486780641
Release Date: 2014-08-20
Genre: Mathematics

This classic of advanced statistics is geared toward graduate-level readers and uses the concepts of gambling to develop important ideas in probability theory. The authors have distilled the essence of many years' research into a dozen concise chapters. "Strongly recommended" by the Journal of the American Statistical Association upon its initial publication, this revised and updated edition features contributions from two well-known statisticians that include a new Preface, updated references, and findings from recent research. Following an introductory chapter, the book formulates the gambler's problem and discusses gambling strategies. Succeeding chapters explore the properties associated with casinos and certain measures of subfairness. Concluding chapters relate the scope of the gambler's problems to more general mathematical ideas, including dynamic programming, Bayesian statistics, and stochastic processes. Dover (2014) revised and updated republication of the 1976 Dover edition entitled Inequalities for Stochastic Processes. See every Dover book in print at www.doverpublications.com

Understanding Markov Chains

Author: Nicolas Privault
Publisher: Springer
ISBN: 9789811306594
Release Date: 2018-08-03
Genre: Mathematics

This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.

Sociophysics An Introduction

Author: Parongama Sen
Publisher: Oxford University Press
ISBN: 9780199662456
Release Date: 2013-10
Genre: Computers

This book discusses the study and analysis of the physical aspects of social systems and models, inspired by the analogy with familiar models of physical systems and possible applications of statistical physics tools. Unlike the traditional analysis of the physics of macroscopic many-body or condensed matter systems, which is now an established and mature subject, the upsurge in the physical analysis and modelling of social systems, which are clearly many-body dynamical systems, is a recent phenomenon. Though the major developments in sociophysics have taken place only recently, the earliest attempts of proposing "Social Physics" as a discipline are more than one and a half centuries old. Various developments in the mainstream physics of condensed matter systems have inspired and induced the recent growth of sociophysical analysis and models. In spite of the tremendous efforts of many scientists in recent years, the subject is still in its infancy and major challenges are yet to be taken up. An introduction to these challenges is the main motivation for this book.

The Foundations of Statistics

Author: Leonard J. Savage
Publisher: Courier Corporation
ISBN: 9780486137100
Release Date: 2012-08-29
Genre: Mathematics

Classic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended.

An Introduction to Stochastic Modeling

Author: Howard M. Taylor
Publisher: Academic Press
ISBN: 9781483220444
Release Date: 2014-05-10
Genre: Mathematics

An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Control Techniques for Complex Networks

Author: Sean Meyn
Publisher: Cambridge University Press
ISBN: 9780521884419
Release Date: 2008
Genre: Computers

From foundations to state-of-the-art; the tools and philosophy you need to build network models.

Modeling with It Stochastic Differential Equations

Author: E. Allen
Publisher: Springer Science & Business Media
ISBN: 9781402059537
Release Date: 2007-03-08
Genre: Mathematics

This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.

Utility and Probability

Author: John Eatwell
Publisher: Springer
ISBN: 9781349205684
Release Date: 1990-02-23
Genre: Business & Economics

This is an excerpt from the 4-volume dictionary of economics, a reference book which aims to define the subject of economics today. 1300 subject entries in the complete work cover the broad themes of economic theory. This extract concentrates on utility and probability.

All of Statistics

Author: Larry Wasserman
Publisher: Springer Science & Business Media
ISBN: 9780387217369
Release Date: 2013-12-11
Genre: Mathematics

Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

Philosophical Dimensions in Mathematics Education

Author: Karen Francois
Publisher: Springer Science & Business Media
ISBN: 9780387715759
Release Date: 2007-11-15
Genre: Education

This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

Probability Statistics and Random Processes For Electrical Engineering

Author: Alberto Leon-Garcia
Publisher: Pearson Higher Ed
ISBN: 9780133002577
Release Date: 2011-11-21
Genre: Computers

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. This is the standard textbook for courses on probability and statistics, not substantially updated. While helping students to develop their problem-solving skills, the author motivates students with practical applications from various areas of ECE that demonstrate the relevance of probability theory to engineering practice. Included are chapter overviews, summaries, checklists of important terms, annotated references, and a wide selection of fully worked-out real-world examples. In this edition, the Computer Methods sections have been updated and substantially enhanced and new problems have been added.

Stochastic Modeling in Economics and Finance

Author: Jitka Dupacova
Publisher: Springer Science & Business Media
ISBN: 9780306481673
Release Date: 2006-04-18
Genre: Mathematics

In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities. Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects. Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study.

Probability with Martingales

Author: David Williams
Publisher: Cambridge University Press
ISBN: 9781139642989
Release Date: 1991-02-14
Genre: Mathematics

Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text. These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercises play a vital rĂ´le. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.

Uniform Distribution of Sequences

Author: L. Kuipers
Publisher: Courier Corporation
ISBN: 9780486149998
Release Date: 2012-05-24
Genre: Mathematics

The theory of uniform distribution began with Weyl's celebrated paper of 1916 and this book summarizes its development through the mid-1970s, with comprehensive coverage of methods and principles. 1974 edition.

Real Analysis and Probability

Author: R. M. Dudley
Publisher: CRC Press
ISBN: 9781351093095
Release Date: 2018-02-01
Genre: Mathematics

Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.