I am a first year physics grad student and I am looking for a book on stochastic processes. I have learned basic statistics and probability in my undergraduate. Recently I read by N.G. VAN KAMPEN and I found it quite condensed and I could not understand it completely( I had bunch of questions when I read the text and didn't know how to figure them out). I hope to find a book with more examples and clear elaboration. Any suggestions? Thanks!

  • $\begingroup$ Have you asked your supervisor? Have you visited your university library? Have you searched the internet? $\endgroup$ – sammy gerbil Dec 30 '16 at 2:48
  • $\begingroup$ I don't have a supervisor right now, but I have found Gradiner's Handbook of Stochastic Method in our library and read part of it. I have read review of some stochastic processes textbook on Amazon, Goodreads and some other forum. After reading these, I was not satisfied with the information I found and didn't know which one fit my situation best, so I post a question here. $\endgroup$ – Xiang Dec 31 '16 at 3:46
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    $\begingroup$ What is it (a bit more precisely) that you are hoping to find? General stochastic processes? Any stochastic processes in particular? Brownian motion, Wiener process and stochastic calculus/differential equations? Link with statistical mechanics? $\endgroup$ – nabla Jan 13 '17 at 12:15
  • $\begingroup$ Read David C. Shimko's book, "Finance in Continuous Time - A Primer". Shockingly good for self teaching, and you don't need to leave physics to learn from it. 54 cents on Amazon ... what can you lose? $\endgroup$ – Paul Young Jan 28 '19 at 0:09

A gentle introduction to the basic ideas of stochastic processes -

  • Stochastic Processes for Physicists: Understanding Noisy Systems by by Kurt Jacobs

The following are excellent reference textbooks -

  • The Fokker-Planck Equation by Hannes Risken
  • Stochastic Methods by Crispin Gardiner

For numerical solution of SDE the following are recommended -

  • Numerical Solution of Stochastic Differential Equations by Kloeden and Platen
  • Numerical Solution of SDE Through Computer Experiments by Kloeden and Platen

Simple explanation about equivalence of Fokker-Planck and Langevin formalism (first two chapters)

  • Nonequilibrium Statistical Mechanics by Robert Zwanzig

The following have a lot of insight about Langevin equation and Brownian motion -

  • The Langevin equation by Coffey, Kalmykov and Waldron
  • Brownian Motion by Mazo

Advanced topics in stochastic energetics (work, heat, etc.) -

  • Stochastic Energetics by Ken Sekimoto

The concept of interpretation in SDE is very important to understand. Its physical content ("spurious drift") confused many good physicists over the years, and is still actively researched. Most books dwell on Ito and Stratonovich interpretations, while many physical systems are anti-Ito (a.k.a. kinetic/Hanggi-Klimontovich). I advice to read through the two articles suggested here after you learn a bit about Ito-Stratonovich dilemma. There is an easy way to transform between them, however you must know first what are you doing.

  • $\begingroup$ This is a very good start but I wonder if you could add more details about the books (as requested in the answering guide. $\endgroup$ – Kyle Kanos Jan 27 '19 at 22:56
  • $\begingroup$ Hi alexander, have you had a chance to read through the answering guide in my previous comment? The list of books is okay, but I'm not really keen on the idea of the bounty going to an answer that doesn't fit community guidelines and would really appreciate you filling out details of the books (e.g., background material, what it covers, depth, level, etc). $\endgroup$ – Kyle Kanos Feb 1 '19 at 3:10
  • $\begingroup$ For reference, only half of the offered bounty was awarded to this post (automatically by the system, not by me) because I think it's an incomplete answer, as it doesn't follow site guidelines on answering resource-recommendation questions. $\endgroup$ – Kyle Kanos Feb 5 '19 at 0:14

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