Topics in
Probability Theory and Stochastic Processes
Steven R. Dunbar
Lessons
Note: In all notes, lessons, tests, quizzes and homework
assignments, unless specifically noted otherwise
 Because the lessons use MathML/xml/xhtml, and because
Firefox is the only common browser with MathML enabled, use
Firefox to view the following lessons.
 Interest is assumed to be compounded continuously.
 The mathematical function log(x) means the natural
logarithm, that is, logarithms to the base e.
Real Analysis Background

Asymptotic Limits
and Series
Updated Monday, 03Oct2011 06:02:34 CDT
Stirling's Formula

Wallis Formula
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Evaluation of the Gaussian Density Integral
Updated Saturday, 22Oct2011 05:49:19 CDT

Stirling's Formula Derived from Elementary Sequences
and Series
Updated Tuesday, 20Sep2011 06:06:46 CDT

Stirling's Formula by Using EulerMaclaurin Summation
Updated Monday, 10Oct2011 06:00:47 CDT

Stirling's Formula from Wallis' Formula and the
Trapezoidal Approximation
Updated Monday, 10Oct2011 06:00:00 CDT

Stirling's Formula Derived from the Gamma Function
Updated Monday, 26Nov2012 05:56:59 CST

Stirling's Formula in Real and Complex Variables
Updated Monday, 23May2011 05:55:15 CDT

Stirling's Formula Derived from the Poisson Distribution
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Bernoulli Trials

Binomial Distribution
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Weak Law of Large Numbers
Updated Wednesday, 25May2011 06:16:28 CDT

Large Deviations
Updated Saturday, 04Jun2011 09:38:07 CDT
Normal Random Variables, Gaussian Distributions

The Sum of Independent Normal Random Variables is Normal
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Brownian Motion

Introduction
to Bernstein Polynomials and Brownian Motion

Bernstein Polynomials and the Weierstrass Approximation Theorem

Bernstein Motions and the convergence to Wiener measure
Central Limit Theorem
Large Deviations
Markov Process Variants
Eigenvalues, Eigenvectors, and Normal Forms of Matrices
Updated Friday, 28May2010 05:47:02 CDT
Fastest Mixing Markov Chain
Updated Friday, 16Apr2010 06:03:37 CDT
Applications, especially with Markov Chains
Worst Case and Average Case Behavior of the Simplex
Algorithm
Updated Thursday, 20Jan2011 21:01:31 CST
Smoothed Analysis for Linear Optimization
Algorithm
Updated Thursday, 27Jan2011 20:52:43 CST
Martingales
>
Weak Law of Large Numbers
Counting and Poisson Processes
Conditional Probability and Expectation
Online Tables for Probability and Cumulative
Distributions
Here are some links to Online Distribution Tables:
 Statsoft
This site has several different distributions in a nice
backofthebooklooking HTML format.
 David
Lane, Rice University, Hyperstat
This links to a Java applet that will compute the percentages for
the normal distribution when given the Z values
Annotated Bibliography
A personal, eclectic and biased
annotated bibliography
of books and articles about probability, stochastic processes
and mathematical finance.
Outside Readings/Links:
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Steve Dunbar's Home
Page, http://www.math.unl.edu/~sdunbar
Email to Steve Dunbar,
sdunbar@unl.edu