This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.
Learning about stochastic processes has been an interesting experience for me. I guess that I'm too much used to determinism in classical physics, so switching to a probabilistic point of view hasn't been that smooth as I would have wanted it to be. Despite that, I found the book quite informative. I spent most of the time studying Markov's processes and all that follows from them (Chapman-Kolmogorov equation, Master equation, Fokker-Planck equation, Langevin equation...), but I think I can give my opinion on the book as a whole.
I'll be honest - it's a book for advanced readers. I feel that undergrad students who happen to take on this book will have a more difficult time, because one need to be well acquainted with probability theory for starters, and then take some grad physics in stride (If you're an undergrad student reading this review: If you want to read this book - you can do it! It might take you more time than someone else who has already heard of the things discussed, but you can do it anyway.). The text in itself was clear enough, but that wasn't the issue. The thing is that lots of expressions were derived using the ellipses method, i.e. the reader has to either know how to derive them him/herself or have additional literature, which is daunting at times. (Especially for those among us who don't spend their free time solving integro-differential equations *cough*) And for that reason alone, I give this book 4 stars - while it undoubtedly has its merits, I felt it was too advanced at certain times.