MATH/STAT 491/498: INTRODUCTION TO STOCHASTIC PROCESSES

MATH/STAT 491/8
INTRODUCTION TO STOCHASTIC PROCESSES

FALL 2018/WINTER 2019


Instructor: Fang Han
E-mail: fanghan@uw.edu
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
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