18.445 | Spring 2015 | Graduate

Introduction to Stochastic Processes

Calendar

SES # TOPICS KEY DATES
1 Introduction to Finite Markov Chains  
2 Markov Chains: Stationary Distribution  
3 Markov Chains: Time-reversal  
4 Introduction to Markov Chain Mixing Problem Set 1 due
5 Stationary Times  
6 Lower Bounds on Mixing Times  
7 Summary on Mixing Times  
8 Random Walk on Networks 1  Problem Set 2 due
9 Random Walk on Networks 2  
10 Hitting Times  
11 Summary on Random Walk on Networks  
12 Countable State Space Chain 1  
13 Countable State Space Chain 2  
14 Midterm Exam  Problem Set 3 due
15 Conditional Expectation and Introduction to Martingales  
16 Martingales: Optional Stopping Theorem  
17 Martingales: Convergence  
18 Martingales: Uniformly Integrable  Problem Set 4 due
19 Galton-Watson Tree  
20 Poisson Process  
21 Continuous Time Markov Chain  
22 Infinitesimal Generator  Problem Set 5 due
23 Irreducible and Recurrence  
24 Stationary Distribution  
25 Final Exam  

Course Info

Instructor
Departments
As Taught In
Spring 2015
Level
Learning Resource Types
Lecture Notes
Problem Sets with Solutions