LTTC Stochastic Processes

Basics

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

• 10.50-12.50; Mondays, 9 October - 6 November
  
• De Morgan House, Russell Square
• Hardy Room (except session 2 - 16 October - that will take place at Room 14 in the 2nd floor)

General links/references

• Materials from 2022

• Videos on YouTube

• Rolling homework

Classes

Class one

We discussed sampling, generating random variables, and the weak law of large numbers. we also introduced coupling.

• Random variables theory and practice
• Law of large numbers and R
• Coupling

Class two

We discussed Markov chains and their convergence properties

• A simple example
• Doeblin’s coupling

Class three

We discussed coupling from the past and von Neumann’s \(L^2\) Ergodic Theorem

• Coupling from the past

• The mean ergodic theorem

Class four

We gave an overview of Poisson process and also discussed independent and deterministic thinning.

• Poisson processes
  • Some exercises

Additional links

• Ball’s paper
• Thinning on finite volumes

Class five

• Strong law of large numbers
• Weierstrass approximation
• Renewal processes

Endnotes

Version: 06 November 2023