Prerequisites: Single variable and multivariable calculus, including sequences and series, partial derivatives and multiple integrals.
The text for this course is Probability and Random Processes, 3rd edition, by Geoffrey Grimmett and David Stirzaker, Oxford University Press. We will cover the first five chapters and portions of the sixth and thirteenth chapter of the text. Topics will include probability spaces, random variables, probability distributions, generating functions, law of large numbers and the central limit theorem, random walks, discrete and continuous Markov processes. Homework will be due once a week (and will be put up on the board in class and posted on the instructor's website). We will have a one hour midterm exam, announced a week in advance. There will be NO MAKEUPS. The final exam will be cumulative, but skewed toward the last half of the term.
For more information about the Basic Probability course, please visit the course website.
Prerequisite: MATH-GA 2901 Basic Probability or equivalent.
Review of basic probability and useful tools. Bernoulli trials and random walk. Law of large numbers and central limit theorem. Conditional expectation and martingales. Brownian motion and its simplest properties. Diffusion in general: forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus. Feynman-Kac and Cameron-Martin Formulas. Applications as time permits.