# probability models springer undergraduate mathematics series

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## Probability Models

**Author :**John Haigh

**ISBN :**9781447153436

**Genre :**Mathematics

**File Size :**37. 18 MB

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The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This textbook contains many worked examples and several chapters have been updated and expanded for the second edition. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.

## Regression

**Author :**N. H. Bingham

**ISBN :**1848829698

**Genre :**Mathematics

**File Size :**36. 1 MB

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Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential. Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions. The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh’s Probability Models, and T. S. Blyth & E.F. Robertsons’ Basic Linear Algebra and Further Linear Algebra.

## Basic Probability Theory With Applications

**Author :**Mario Lefebvre

**ISBN :**9780387749952

**Genre :**Mathematics

**File Size :**56. 46 MB

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The main intended audience for this book is undergraduate students in pure and applied sciences, especially those in engineering. Chapters 2 to 4 cover the probability theory they generally need in their training. Although the treatment of the subject is surely su?cient for non-mathematicians, I intentionally avoided getting too much into detail. For instance, topics such as mixed type random variables and the Dirac delta function are only brie?y mentioned. Courses on probability theory are often considered di?cult. However, after having taught this subject for many years, I have come to the conclusion that one of the biggest problems that the students face when they try to learn probability theory, particularly nowadays, is their de?ciencies in basic di?erential and integral calculus. Integration by parts, for example, is often already forgotten by the students when they take a course on probability. For this reason, I have decided to write a chapter reviewing the basic elements of di?erential calculus. Even though this chapter might not be covered in class, the students can refer to it when needed. In this chapter, an e?ort was made to give the readers a good idea of the use in probability theory of the concepts they should already know. Chapter 2 presents the main results of what is known as elementary probability, including Bayes’ rule and elements of combinatorial analysis.

## Measure Integral And Probability

**Author :**Marek Capinski

**ISBN :**9781447136316

**Genre :**Mathematics

**File Size :**39. 47 MB

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This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

## Understanding Markov Chains

**Author :**Nicolas Privault

**ISBN :**9789814451512

**Genre :**Mathematics

**File Size :**71. 61 MB

**Format :**PDF

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This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.

## An Introduction To Probabilistic Modeling

**Author :**Pierre Bremaud

**ISBN :**9781461210467

**Genre :**Mathematics

**File Size :**81. 84 MB

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Introduction to the basic concepts of probability theory: independence, expectation, convergence in law and almost-sure convergence. Short expositions of more advanced topics such as Markov Chains, Stochastic Processes, Bayesian Decision Theory and Information Theory.

## Basic Stochastic Processes

**Author :**Zdzislaw Brzezniak

**ISBN :**9781447105336

**Genre :**Mathematics

**File Size :**75. 31 MB

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Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.

## Derivative Pricing In Discrete Time

**Author :**Nigel J. Cutland

**ISBN :**9781447144076

**Genre :**Mathematics

**File Size :**77. 64 MB

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Derivatives are financial entities whose value is derived from the value of other more concrete assets such as stocks and commodities. They are an important ingredient of modern financial markets. This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative. To keep the mathematics as simple as possible, while explaining the basic principles, only discrete time models with a finite number of possible future scenarios are considered. The theory examines the simplest possible financial model having only one time step, where many of the fundamental ideas occur, and are easily understood. Proceeding slowly, the theory progresses to more realistic models with several stocks and multiple time steps, and includes a comprehensive treatment of incomplete models. The emphasis throughout is on clarity combined with full rigour. The later chapters deal with more advanced topics, including how the discrete time theory is related to the famous continuous time Black-Scholes theory, and a uniquely thorough treatment of American options. The book assumes no prior knowledge of financial markets, and the mathematical prerequisites are limited to elementary linear algebra and probability. This makes it accessible to undergraduates in mathematics as well as students of other disciplines with a mathematical component. It includes numerous worked examples and exercises, making it suitable for self-study.

## Mathematics For Finance

**Author :**Marek Capinski

**ISBN :**9781852338466

**Genre :**Business & Economics

**File Size :**21. 36 MB

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This textbook contains the fundamentals for an undergraduate course in mathematical finance aimed primarily at students of mathematics. Assuming only a basic knowledge of probability and calculus, the material is presented in a mathematically rigorous and complete way. The book covers the time value of money, including the time structure of interest rates, bonds and stock valuation; derivative securities (futures, options), modelling in discrete time, pricing and hedging, and many other core topics. With numerous examples, problems and exercises, this book is ideally suited for independent study.

## Discrete Probability

**Author :**Hugh Gordon

**ISBN :**9781461219668

**Genre :**Mathematics

**File Size :**63. 3 MB

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Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics. Since calculus is used only occasionally in the text, students who have forgotten their calculus can nevertheless easily understand the book, and its slow, gentle style and clear exposition will also appeal. Basic concepts such as counting, independence, conditional probability, random variables, approximation of probabilities, generating functions, random walks and Markov chains are all clearly explained and backed by many worked exercises. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book, and throughout, there are various historical comments on the study of probability. These include biographical information on such famous contributors as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, and Markov. Of interest to a wide range of readers and useful in many undergraduate programs.