Stochastic Processes II

Department: 
MATH
Course Number: 
4222
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Typically every spring

Renewal theory, Poisson processes and continuous time Markov processes, including an introduction to Brownian motion and martingales

Prerequisites: 
Course Text: 

At the level of Introduction to Stochastic Processes, Lawler, 2nd edition or Introduction to Probability Models, Ross, 10th edition

Topic Outline: 
  • Introduction to Renewal Theory Renewal Theorem, Wald's Theorem, applications in random walk and use of generating functions especially for nonsymmetric walks
  • Introduction to counting processes especially the Poisson process Renewal counting process and renewal time process
  • Continuous time Markov chains (jump processes) Birth and death process Reversed process and applications Brownian motion (Wiener process) Introduction to second order theory Transformation of Gaussian processes Stochastic differential equations Introduction to martingales