Jiaze Qiu
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STAT 171 | Spring 2021

Introduction to Stochastic Processes

Welcome to STAT 171: ​Introduction to Stochastic Processes!

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​
A drunk man will find his way home, but a drunk bird may get lost forever.

-- Shizuo Kakutani
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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
Zoom Link for Jiaze's Section & OH
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
  • ​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
  • ​​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
  • 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
Contact

Jiaze Qiu
Science Center 316.07
One Oxford Street
Cambridge, MA 02138
jiazeqiu@g.harvard.edu
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