## e-books in Theory Of Probability category

**Random Walks and Electric Networks**

by

**Peter G. Doyle, J. Laurie Snell**-

**Dartmouth College**,

**2006**

In this work we will look at the interplay of physics and mathematics in terms of an example where the mathematics involved is at the college level. The example is the relation between elementary electric network theory and random walks.

(

**1417**views)

**The Logic Of Chance**

by

**John Venn**-

**Macmillan And Company**,

**1888**

No mathematical background is necessary for this classic of probability theory. It remains unsurpassed in its clarity, readability, and charm. It commences with physical foundations, examines logical superstructure, and explores various applications.

(

**1141**views)

**Probability**

by

**Douglas Kennedy**-

**Trinity College**,

**2010**

This material was made available for the course Probability of the Mathematical Tripos. Contents: Basic Concepts; Axiomatic Probability; Discrete Random Variables; Continuous Random Variables; Inequalities, Limit Theorems and Geometric Probability.

(

**1112**views)

**Probability on Trees and Networks**

by

**Russell Lyons, Yuval Peres**-

**Cambridge University Press**,

**2016**

This book is concerned with certain aspects of discrete probability on infinite graphs that are currently in vigorous development. Of course, finite graphs are analyzed as well, but usually with the aim of understanding infinite graphs and networks.

(

**1165**views)

**Extracting Information from Random Data**

by

**Pawel J. Szablowski**-

**arXiv**,

**2016**

We formulate conditions for convergence of Laws of Large Numbers and show its links with of parts mathematical analysis such as summation theory, convergence of orthogonal series. We present also various applications of Law of Large Numbers.

(

**1025**views)

**Probability Course**

by

**Gian-Carlo Rota**-

**David Ellerman**,

**1998**

In 1999, Gian-Carlo Rota gave his famous course, Probability, at MIT for the last time. The late John N. Guidi taped the lectures and took notes which he then wrote up in a verbatim manner conveying the substance and the atmosphere of the course.

(

**1862**views)

**Probability Theory**

by

**Curtis T. McMullen**-

**Harvard University**,

**2011**

Contents: The Sample Space; Elements of Combinatorial Analysis; Random Walks; Combinations of Events; Conditional Probability; The Binomial and Poisson Distributions; Normal Approximation; Unlimited Sequences of Bernoulli Trials; etc.

(

**5517**views)

**Lectures on Elementary Probability**

by

**William G. Faris**-

**University of Arizona**,

**2002**

From the table of contents: Combinatorics; Probability Axioms; Discrete Random Variables; The Bernoulli Process; Continuous Random Variables; The Poisson Process; The weak law of large numbers; The central limit theorem; Estimation.

(

**4572**views)

**Lectures on Integrable Probability**

by

**Alexei Borodin, Vadim Gorin**-

**arXiv**,

**2012**

Topics include integrable models of random growth, determinantal point processes, Schur processes and Markov dynamics on them, Macdonald processes and their application to asymptotics of directed polymers in random media.

(

**3301**views)

**Lecture Notes on Free Probability**

by

**Vladislav Kargin**-

**arXiv**,

**2013**

Contents: Non-commutative Probability Spaces; Distributions; Freeness; Asymptotic Freeness of Random Matrices; Asymptotic Freeness of Haar Unitary Matrices; Free Products of Probability Spaces; Law of Addition; Limit Theorems; Multivariate CLT; etc.

(

**3631**views)

**Introduction to Probability**

by

**Davar Khoshnevisan, Firas Rassoul-Agha**-

**University of Utah**,

**2012**

This is a first course in undergraduate probability. It covers standard material such as combinatorial problems, random variables, distributions, independence, conditional probability, expected value and moments, law of large numbers, etc.

(

**6725**views)

**Introduction to Probability**

by

**Leif Mejlbro**-

**BookBoon**,

**2009**

In this book you will find the basic mathematics of probability theory that is needed by engineers and university students. Topics as Elementary probability calculus, density functions and stochastic processes are illustrated.

(

**5838**views)

**Advanced Topics in Probability**

by

**S.R.S. Varadhan**-

**New York University**,

**2011**

Topics: Brownian Motion; Diffusion Processes; Weak convergence and Compactness; Stochastic Integrals and Ito's formula; Markov Processes, Kolmogorov's equations; Stochastic Differential Equations; Existence and Uniqueness; Girsanov Formula; etc.

(

**5191**views)

**Recent Progress on the Random Conductance Model**

by

**Marek Biskup**-

**arXiv**,

**2012**

Recent progress on understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the environment.

(

**4737**views)

**Applied Probability**

by

**Paul E Pfeiffer**-

**Connexions**,

**2008**

This textbook covers most aspects of advanced and applied probability. The book utilizes a number of user defined m-programs, in combination with built in MATLAB functions, for solving a variety of probabilistic problems.

(

**6954**views)

**Continuous Distributions**

by

**Leif Mejlbro**-

**BookBoon**,

**2009**

Contents: Some theoretical background; Exponential Distribution; The Normal Distribution; Central Limit Theorem; Maxwell distribution; Gamma distribution; Normal distribution and Gamma distribution; Convergence in distribution; 2 distribution; etc.

(

**4894**views)

**Probability Theory and Stochastic Processes with Applications**

by

**Oliver Knill**-

**Overseas Press**,

**2009**

This text covers material of a basic probability course, discrete stochastic processes including Martingale theory, continuous time stochastic processes like Brownian motion and stochastic differential equations, estimation theory, and more.

(

**6139**views)

**Lectures on Measure Theory and Probability**

by

**H.R. Pitt**-

**Tata institute of Fundamental Research**,

**1958**

Measure Theory (Sets and operations on sets, Classical Lebesgue and Stieltjes measures, Lebesgue integral); Probability (Function of a random variable, Conditional probabilities, Central Limit Problem, Random Sequences and Convergence Properties).

(

**7224**views)

**Lectures on Random Polymers**

by

**F. Caravenna, F. den Hollander, N. Petrelis**-

**arXiv**,

**2011**

These lecture notes are a guided tour through the fascinating world of polymer chains interacting with themselves and/or with their environment. The focus is on the mathematical description of a number of physical and chemical phenomena.

(

**6740**views)

**A Probability Course for the Actuaries**

by

**Marcel B. Finan**-

**Arkansas Tech University**,

**2011**

This manuscript will help students prepare for the Probability Exam, the examination administered by the Society of Actuaries. This examination tests a student's knowledge of the fundamental probability tools for quantitatively assessing risk.

(

**6829**views)

**Random Graphs and Complex Networks**

by

**Remco van der Hofstad**-

**Eindhoven University of Technology**,

**2010**

These lecture notes are intended to be used for master courses, where the students have a limited prior knowledge of special topics in probability. We have included many of the preliminaries, such as convergence of random variables, etc.

(

**5522**views)

**Introduction to Stochastic Analysis**

by

**Michael Roeckner**-

**Universitaet Bielefeld**,

**2011**

From the table of contents: Introduction to Pathwise Ito-Calculus; (Semi-)Martingales and Stochastic Integration; Markov Processes and Semigroups - Application to Brownian Motion; Girsanov Transformation; Time Transformation.

(

**5676**views)

**Probability: Theory and Examples**

by

**Rick Durrett**-

**Cambridge University Press**,

**2010**

An introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It concentrates on the results that are the most useful for applications.

(

**7597**views)

**Stochastic Processes**

by

**David Nualart**-

**Universitat de Barcelona**,

**2003**

From the table of contents: Stochastic Processes (Probability Spaces and Random Variables, Definitions and Examples); Jump Processes (The Poisson Process, Superposition of Poisson Processes); Markov Chains; Martingales; Stochastic Calculus.

(

**6395**views)

**Probability for Finance**

by

**Patrick Roger**-

**BookBoon**,

**2010**

The book is intended to be a technical support for students in finance. Topics: Probability spaces and random variables; Moments of a random variable; Usual probability distributions in financial models; Conditional expectations and Limit theorems.

(

**7772**views)

**Almost None of the Theory of Stochastic Processes**

by

**Cosma Rohilla Shalizi**-

**Carnegie Mellon University**,

**2010**

Text for a second course in stochastic processes. It is assumed that you have had a first course on stochastic processes, using elementary probability theory. You will study stochastic processes within the framework of measure-theoretic probability.

(

**6758**views)

**Chance and Luck**

by

**Richard A. Proctor**-

**Longmans, Green, and Co.**,

**1887**

This book contains a discussion of the laws of luck, coincidences, wagers, lotteries and the fallacies of gambling, notes on poker and martingales, explaining in detail the law of probability, the types of gambling, classification of gamblers, etc.

(

**7838**views)

**A Treatise on Probability**

by

**John Maynard Keynes**-

**Macmillan and co**,

**1921**

From the table of contents: Fundamental ideas - The Meaning of Probability, The Measurement of Probabilities; Fundamental theorems; Induction and analogy; Some philosophical applications of probability; The foundations of statistical inference, etc.

(

**7876**views)

**Discrete Distributions**

by

**Leif Mejlbro**-

**BookBoon**,

**2009**

From the table of contents: Some theoretical background; The binomial distribution; The Poisson distribution; The geometric distribution; The Pascal distribution; The negative binomial distribution; The hypergeometric distribution.

(

**8173**views)

**Basic Probability Theory**

by

**Robert B. Ash**-

**Dover Publications**,

**2008**

This text surveys random variables, conditional probability and expectation, characteristic functions, infinite sequences of random variables, Markov chains, and an introduction to statistics. Geared toward advanced undergraduates and graduates.

(

**9323**views)

**Probability Theory**

by

**S. R. S. Varadhan**-

**New York University**,

**2000**

These notes are based on a first year graduate course on Probability and Limit theorems given at Courant Institute of Mathematical Sciences. The text covers discrete time processes. A small amount of measure theory is included.

(

**13208**views)

**Probability, Geometry and Integrable Systems**

by

**Mark Pinsky, Bjorn Birnir**-

**Cambridge University Press**,

**2007**

The three main themes of this book are probability theory, differential geometry, and the theory of integrable systems. The papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems.

(

**9784**views)

**Probability Theory: The Logic of Science**

by

**E. T. Jaynes**-

**Cambridge University Press**,

**2002**

The book is addressed to readers familiar with applied mathematics at the advanced undergraduate level. The text is concerned with probability theory and all of its mathematics, but now viewed in a wider context than that of the standard textbooks.

(

**9470**views)

**Probability, Random Processes, and Ergodic Properties**

by

**Robert M. Gray**-

**Springer**,

**2008**

A self-contained treatment of the theory of probability, random processes. It is intended to lay theoretical foundations for measure and integration theory, and to develop the long term time average behavior of measurements made on random processes.

(

**8878**views)

**A Philosophical Essay on Probabilities**

by

**Pierre Simon Laplace**-

**Chapman & Hall**,

**1902**

Classic book on probability theory. It demonstrates, without the use of higher mathematics, the application of probability to games of chance, physics, reliability of witnesses, astronomy, insurance, democratic government, and many other areas.

(

**12278**views)

**A History Of The Mathematical Theory Of Probability**

by

**I. Todhunter**-

**Kessinger Publishing, LLC**,

**2007**

History of the probability theory from the time of Pascal to that of Laplace (1865). Todhunter gave a close account of the difficulties involved and the solutions offered by each investigator. His studies were thorough and fully documented.

(

**12931**views)

**Radically Elementary Probability Theory**

by

**Edward Nelson**-

**Princeton University Press**,

**1987**

In this book Nelson develops a new approach to probability theory that is just as powerful as but much simpler than conventional Kolmogorov-style probability theory used throughout mathematics for most of the 20th century.

(

**12247**views)

**An Introduction to Probability and Random Processes**

by

**Gian-Carlo Rota, Kenneth Baclawski**,

**1979**

The purpose of the text is to learn to think probabilistically. The book starts by giving a bird's-eye view of probability, it first examines a number of the great unsolved problems of probability theory to get a feeling for the field.

(

**12839**views)

**Introduction to Probability**

by

**C. M. Grinstead, J. L. Snell**-

**American Mathematical Society**,

**1997**

The textbook for an introductory course in probability for students of mathematics, physics, engineering, social sciences, and computer science. It presents a thorough treatment of techniques necessary for a good understanding of the subject.

(

**54975**views)