Notes for Math 450 Lecture Notes 2 Renato Feres 1 Probability Spaces

Notes for Math 450 Lecture Notes 3

We introduce some of the standard parameters associated to a random variable. The two most common are the expected value and the variance. These are special cases of moments of a probability distribution. Before defining these quantities, it may be helpful to recall some basic concepts associated to random variables.

Supplementary notes for Math 495 Renato Feres

How many times should you shuffle a deck of cards?

These are notes for the course Math 450 Random Processes, taught during the spring 07 semester at Washington University, and for a talk given at the Wash. U. undergraduate math club. We look at the subject of random walks on the symmetric group and card shuffling from an “experimental” viewpoint.

Notes for Math 450 Elements of Stochastic Calculus

These notes supplement the paper by Higham and provide more information on the basic ideas of stochastic calculus and stochastic differential equations. You will need some of this material for homework assignment 12 in addition to Higham’s paper. There are many places where you can find this theory developed in greater detail and better than here. See, for example, [CKO]. Also note that the inf...

Notes for Math 450 Continuous-time Markov chains and Stochastic Simulation

These notes are intended to serve as a guide to chapter 2 of Norris’s textbook. We also list a few programs for use in the simulation assignments. As always, we fix the probability space (Ω,F , P ). All random variables should be regarded as F-measurable functions on Ω. Let S be a countable (or finite) state set, typically a subset of Z. A continuous-time random process (Xt)t≥0 is a family of r...