Welcome to STAT 171: Introduction to Stochastic Processes!
|
A drunk man will find his way home, but a drunk bird may get lost forever. -- Shizuo Kakutani |
|
Basic Information
Course Number and Course Name |
STAT 171: Introduction to Stochastic Processes |
Instructor / TF |
Subhabrata Sen / Jiaze Qiu / Fernando Vicente |
Email |
jiazeqiu@g.harvard.edu |
Sections (Jiaze) |
Wednesdays 9pm-10pm (ET) |
Office Hours (Jiaze) |
Wednesdays 10pm-Midnight (ET) |
Zoom |
Please feel free to contact me if you have any question. I will try to reply as soon as possible.
Schedule
- Week 1, Jan 27 (Handout, Solution)
- STAT 110 review
- A very brief introduction to R and R Studio
- Week 2, Feb 3 (Handout, Solution)
- Markov Property
- Stochastic / One-step Transition / Markov Matrix
- Limiting distribution & Stationary distribution
- Week 3, Feb 10 (Handout, Solution)
- Communication class & Reducibility
- Recurrence & Transience
- Periodicity
- Fundamental Theorem of Ergodic Markov Chains (and two other related theorems)
- Time Reversibility
- Communication class & Reducibility
- Week 4, Feb 17 (Handout, Solution)
- Branching process
- Week 5, Feb 24 (Handout, Solution)
- Midterm 1 review
- Week 6, Mar 3 (Handout, Solution)
- MCMC baiscs
- Metropolis-Hastings
- Gibbs sampler
- TV distance
- Spectral conditions for convergence of Markov Chain
- Week 7, Mar 10 (Handout, Solution)
- Poisson Processes
- Midterm 1 Question 4 (b)
- Week 8, Mar 17 (Handout, Solution)
- Continuous-time Markov Chains
- Transition function
- Holding times and embedded chains
- Transition rates (alarm clocks)
- Long-term behavior
- Continuous-time Markov Chains
- Week 9, Mar 24 (Handout, Solution)
- Martingale
- Stopping time (Preview)
- Week 10: Please note I will not hold section or OH this week due to overlap with midterm schedule. In the meantime, Fernando's Monday section will go on as usual. (Handout, Solution)
- Midterm 2 review
- Week 11, Apr 7 (Handout, Solution)
- Brownian Motion
- Definition
- Martingale
- Reflection Principle
- Stopping Time
- Strong Markov property
- General Markov Process
- Brownian Motion
- Week 12, Apr 13 (Handout, Solution)
- OST and Brownian motion
- Brownian Bridge
- Geometric Brownian motion
- Applications in finance
- Week 13, Apr 20 (Handout, Solution)
- Introduction to Stochastic Calculus
- Week 14, Apr 27 (Handout, Solution)
- Ito's lemma
- Introduction to SDE
|
Back to TEACHING
|