Applied Markov Processes

Information

• Lecturer: Prof. Hugo Touchette
• The course is based on Python for simulations
• Course information
• SU course code: MS763 Honours

References

• G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Oxford, 2001.
• K. Jacobs, Stochastic Processes for Physicists, Cambridge, 2010.
• Z. Brzezniak and T. Zastawniak, Basic Stochastic Processes, Springer, New York, 1999.
• C. W. Gardiner, Handbook of Stochastic Methods for Physics, Springer, New York, 1985.
• H. M. Taylor and S. Karlin, An Introduction to Stochastic Modeling, Academic Press, New York, 1998.
• G. A. Pavliotis, Stochastic Processes and Applications, Springer, New York, 2014.

Lecture notes

• Chapter 1: Probability theory and sampling
• Chapter 2: Discrete-time Markov chains
• Chapter 3: Continuous-time Markov chains
• Chapter 4: Brownian motion
• Chapter 5: Stochastic differential equations

Courseworks

Solutions and Python code available on demand.

• CW1: Probability theory and sampling
• CW2: Discrete-time Markov chains
• CW3: Continuous-time Markov chains
• CW4: Brownian motion
• CW5: Stochastic differential equations

Tutorials

• Python interactive tutorial
• Introduction to Python with Jupyter by Maxime Sangnier, Paris University
• Plotting in Python by Maxime Sangnier, Paris University
• Scientific computing in Python by Maxime Sangnier, Paris University
• Fast intro to Mathematica for maths students
• DataCamp free introduction to Python

Resources and links

• List of Python commands (cheat sheet)
• Mathematica commands
• Matlab commands
• List of random number generators
• Histograms in Python
• Metropolis et al. paper
• Hastings's paper

Software installation

• Python and Jupyter notebook
• Project Jupyter instructions
• Jupyter installation manual
• You can use either Jupyter notebook or Jupyter lab (nicer)
• Matlab: SU has a campus wide license so anyone can download and install it.
• Create account on MathWorks with your SU email address
• Log in in your account
• Download Matlab from there
• Mathematica: SU has a campus wide licence.
• Create account on Wolfram with your SU email address
• Log in in your account
• Download Mathematica from there