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So I have a background in statistics and differential equations, but not much physics at all. But I am working on a project relating to stochastic differential equations and Markov processes. I was hoping that someone could point out a good undergraduate level book on the master equation and the Fokker-Planck equation and the underlying intuition.

Now I imagine that most undergraduates don't have enough mathematical background to work on master equations and the Fokker-Planck equation. However, I was hoping to find something that was elementary or a good introduction--instead of a graduate text that assumed I had seen that material before.

One thing I find confusing about some treatments of the master equation is that the physics methods and the probability methods are the same, but with a different name. So like the Chapman-Kolmogorov equation is a discrete form of the Master equation, which is simple enough. The Sheldon Ross book has a very good treatment of the Chapman-Kolmogorov equation. But beyond that most texts just jump into a lot of formalism and little explanation.

If anyone knows of some good videos on these topics, that would be appreciated as well. Sometimes videos cover the material with a nicer explanation.

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    $\begingroup$ Try van Kampen's Stochastic Processes in Physics and Chemistry! $\endgroup$
    – knzhou
    Commented Dec 19, 2020 at 23:27
  • $\begingroup$ @knzhou thanks for the suggestion. I will definitely take a look at that book. The reviews seem very positive, so hopefully that will help clarify my confusions :). Thanks again. $\endgroup$
    – krishnab
    Commented Dec 20, 2020 at 0:32
  • $\begingroup$ I find Van Kampen rather terse. For introductions I suggest Gillespie's "Markov processes for scientists and engineers". It's simple and self-contained. More nuanced presentations for researchers are Risken's "The Fokker-Planck equation" and Gardiner's "Stochastic processes in the physical sciences". You might also look at Weiss's "Aspects and Applications of the Random Walk" and Cox &Miller's "Stochastic processes" These books are essential reading for researchers in master equations and related topics. $\endgroup$
    – kevinkayaks
    Commented Jan 27, 2021 at 18:39
  • $\begingroup$ Now that I read more carefully about your background, you should get the gardiner book. For videos, see Balakrishnan's IIT Madras lectures on Stochastic processes on youtube. He is excellent. His early papers are also quite pedagogical. $\endgroup$
    – kevinkayaks
    Commented Jan 27, 2021 at 18:42

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