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!
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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.