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Extracting Information from Random DataExtracting 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.

Probability CourseProbability 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.

Probability TheoryProbability 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.

Lectures on Elementary ProbabilityLectures 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.

Lectures on Integrable ProbabilityLectures 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.

Lecture Notes on Free ProbabilityLecture 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.

Introduction to ProbabilityIntroduction 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.

Introduction to ProbabilityIntroduction 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.

Advanced Topics in ProbabilityAdvanced 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.

Recent Progress on the Random Conductance ModelRecent 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.

Applied ProbabilityApplied 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.

Continuous DistributionsContinuous 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.

Probability Theory and Stochastic Processes with ApplicationsProbability 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.

Lectures on Measure Theory and ProbabilityLectures 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).

Lectures on Random PolymersLectures 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.

A Probability Course for the ActuariesA 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.

Random Graphs and Complex NetworksRandom 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.

Introduction to Stochastic AnalysisIntroduction 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.

Probability: Theory and ExamplesProbability: 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.

Stochastic ProcessesStochastic 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.

Probability for FinanceProbability 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.

Almost None of the Theory of Stochastic ProcessesAlmost 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.

Chance and LuckChance 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.

A Treatise on ProbabilityA 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.

Discrete DistributionsDiscrete 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.

Basic Probability TheoryBasic 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.

Probability TheoryProbability 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.

Probability, Geometry and Integrable SystemsProbability, 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.

Probability Theory: The Logic of ScienceProbability 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.

Probability, Random Processes, and Ergodic PropertiesProbability, 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.

A Philosophical Essay on ProbabilitiesA 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.

A History Of The Mathematical Theory Of ProbabilityA 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.

Radically Elementary Probability TheoryRadically 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.

An Introduction to Probability and Random ProcessesAn 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.

Introduction to ProbabilityIntroduction 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.