LTTC Stochastic Processes

• Current 2023 website

Basics

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

• 10.50-12.50; Mondays, 3 October - 31 October
  

• De Morgan House, Russell Square

• The lectures are now completed. I will be in contact with you in 2023 regarding the light assessment. It was my pleasure to be your lecturer.

General links/references

• Materials from 2021

• Videos on YouTube

• Rolling homework

Classes

• Class 1: Introduction to random number generation, R, Python, and the weak law of large numbers.

  • Intro to R

  • Intro to Python

  • Random variables, theory and practice

  • Law of large numbers and R

• Class 2: Rejection sampling, Integration, Weierstrass approximation theorem

  • Weierstrass

• Class 3: Markov chains and their convergence

  • Introduction
  • Coupling
    • You always knew coupling
  • Doeblin’s coupling

• Class 4: Markov chains and Poisson point processes

  • We continued our discussion of Markov chains and their convergence
  • Poisson processes on finite volumes
    • Clarke’s application
      • More discussion

• Class 5: Poisson processes continued

  • Continuous-time Markov chains (Optional)

Some code that might have been discussed in class

• Time for the sum to exceed (Pen and Paper)

• Rejection sampling on a disc (Section 8)

• Von Neumann fair bit extractor

• Integration

• Random triangles

• Symbolic computing and a general two state Markov chain

• Data from a MC

• Shiny app for Poisson process

  • Source

• Poisson process on a sphere

• Vertex reinforced random walk

  • Optional materials to help understand trapping

Endnotes

Version: 08 October 2023