LTTC Stochastic Processes

Mock exam

Link

Basics

Instructor: Terry Soo
email: t.soo@ucl.ac.uk
My homepage
Original posting

• 10.30-12.30; Mondays, starting November 8
  
• UCL Cruciform B304 (weeks 1-4)
• UCL Physics A1/3 (week 5)
• Zoom link (when available)
• Office hours, by request, most likely will be Zoom

General links/references

• Related materials from UCL Stat 9 2021

• Related materials from UCL Stat 9 2020

• Extra reading and references

Schedule

• Week1: Introductions; Review of probability theory
  • Recording; you may need to manually download to see the entire video.
• Week2: Weierstrass approximation, the strong law, coupling and total variational distance.
  • Recording
    • I believe that I technically only proved the Bernstein polynomials converged pointwise, and did not argue enough that the convergence is uniform; for this, you really need to use Markov’s inequality and notice that the variance is maximized at \(p=\tfrac{1}{2}\); see the notes for details.
      
• Week3: Markov chains and Doeblin’s coupling.
  • Recording
• Week4: Law of large numbers for Markov chains
  • Recording
• Week5: Poisson processes
  • Recording (only first half available)

Lecture notes

• Re-introduction to probability theory (mostly review)
  • Sample spaces
  • Random variables I
  • Random variables II
  • Expectation (discrete)
  • Expectation (continuous)
• Probability and R
• Weierstrass approximation
• The strong law of large numbers
• Coupling and total variational distance
• Review of Markov chains
• Coupling and the long term behaviour of Markov chains
• Poisson processes
• Continuous-time Markov chains
• Renewal processes

Other materials

• Rolling Homework

• Worked exercises for Poisson processes

• Introduction to R

• Introduction to Python

• Possibly related videos on YouTube (made for UCL Stat9)

Endnotes

Version: 06 March 2022