# Professor Karl Sigman's Lecture Notes on Monte Carlo Simulation

**Instructor:**
Professor Karl Sigman

Department of Industrial Engineering and Operations Research

Phone: (212) 854-3556

FAX: (212) 854-8103

karl.sigman@columbia.edu

http://www.columbia.edu/~ks20

COURSE WEB SITE:
http://www.columbia.edu/~ks20/4703-Sigman/Monte-Carlo-Sigman.html
### Lecture Notes

- The acceptance rejection method with applications;
generating a standard normal random variable
- Simulating Brownian motion and geometric
Brownian motion in one and two dimensions
- Simulation of Markov chains
- Introduction to variance reduction methods
- Simulating renewal processes,
Poisson processes (stationary and non-stationary), compound Poisson processes
- Introduction to estimating sensitivites such as the Greeks
(sample-path method, score function method, finite-difference method)
- Importance sampling