INTRODUCTION TO STOCHASTIC PROCESSES
FALL 2018/WINTER 2019
Instructor: Fang Han
Lectures: MWF: 1130-1220 MEB 242
MATH/STAT 491/8 is a two-quarter course sequence in place of MATH/STAT 491/2 for the B.S. in Mathematics degree option.
The sequence provides a relatively complete introduction to core problems in stochastic processes.
These provide answers to questions such as:
- Why is a drunken person (who is capable of staying on their feet) unlikely to walk very far?
- On average, could a gambler gain something by stopping play based on the information obtained so far?
- Is there much difference in terms of waiting time if there is only one or multiple servers in the line?
- How do we understand the observed motion of small particles immersed in water?
- How do we understand the stock market? Why do we study logarithmic returns? Why is Brownian motion used as a model?
- How do stochastic processes results help solve statistics and machine learning problems?
Tentative outline of topics covered:
- Probability basics
- Random walk and martingales
- Markov chains
- Poisson processes
- Brownian motion
- Applications to statistics/machine learning