link to University of Nebraska Lincoln
Department of Mathematics
203 Avery Hall
University of Nebraska Lincoln
Lincoln, NE 68588-0323
402-472-3731 (voice)
402-472-8466 (fax)

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

  1. 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.
  2. Interest is assumed to be compounded continuously.
  3. The mathematical function log(x) means the natural logarithm, that is, logarithms to the base e.

Real Analysis Background

  1. Asymptotic Limits and Series
    Updated Monday, 03-Oct-2011 06:02:34 CDT

Stirling's Formula

  1. Wallis Formula
    Updated [an error occurred while processing this directive]
  2. Evaluation of the Gaussian Density Integral
    Updated Saturday, 22-Oct-2011 05:49:19 CDT
  3. Stirling's Formula Derived from Elementary Sequences and Series
    Updated Tuesday, 20-Sep-2011 06:06:46 CDT
  4. Stirling's Formula by Using Euler-Maclaurin Summation
    Updated Monday, 10-Oct-2011 06:00:47 CDT
  5. Stirling's Formula from Wallis' Formula and the Trapezoidal Approximation
    Updated Monday, 10-Oct-2011 06:00:00 CDT
  6. Stirling's Formula Derived from the Gamma Function
    Updated Monday, 26-Nov-2012 05:56:59 CST
  7. Stirling's Formula in Real and Complex Variables
    Updated Monday, 23-May-2011 05:55:15 CDT
  8. Stirling's Formula Derived from the Poisson Distribution
    Updated [an error occurred while processing this directive]

Bernoulli Trials

  1. Binomial Distribution
    Updated [an error occurred while processing this directive]
  2. Weak Law of Large Numbers
    Updated Wednesday, 25-May-2011 06:16:28 CDT
  3. Large Deviations
    Updated Saturday, 04-Jun-2011 09:38:07 CDT

Normal Random Variables, Gaussian Distributions

  1. The Sum of Independent Normal Random Variables is Normal
  2. Updated [an error occurred while processing this directive]

Brownian Motion

  1. Introduction to Bernstein Polynomials and Brownian Motion
  2. Bernstein Polynomials and the Weierstrass Approximation Theorem
  3. 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, 28-May-2010 05:47:02 CDT


Fastest Mixing Markov Chain
Updated Friday, 16-Apr-2010 06:03:37 CDT

Applications, especially with Markov Chains

Worst Case and Average Case Behavior of the Simplex Algorithm
Updated Thursday, 20-Jan-2011 21:01:31 CST

Smoothed Analysis for Linear Optimization Algorithm
Updated Thursday, 27-Jan-2011 20:52:43 CST

Martingales

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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:
  1. Statsoft This site has several different distributions in a nice back-of-the-book-looking HTML format.
  2. 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 ] Steve Dunbar's Home Page, http://www.math.unl.edu/~sdunbar
[ Email to Steve Dunbar ] Email to Steve Dunbar, sdunbar@unl.edu