Good books on stochastic processes?

camel_jockey

Hey!

Just as the title suggests I am looking for a good book on stochastic processes which isn't just praised because it is used everywhere, but because the students actually find it thorough, crystal-clear and attentive to detail. Hopefully with solved exercises and problems too!

Anyone know of such a title?

Would be most grateful :)

Stephen Tashi

You'll get better advice if you specify what your current understanding of probability theory is.

Stochastic processes is a very wide field. It isn't clear whether your idea of a "stochastic process" is completely general or specialized. For example, people interested in financial models are often interested in stochastic differential equations, the Ito calculus etc.

lavinia

Karlin and Taylor's books are wonderful and general.

I agree that if you have a specific goal then narrower scoped books might be better.

For a soft introduction to derivatives pricing, Financial Calculus by Baxter and Rennie gives excellent descriptions of what you need to know about Brownian motion, Ito's Lemma, and conditional probability to price derivative. It is also fascinating to see how differential equations for options prices arise from Brownian motions and and no arbitrage arguments.

A book I like - and it is very small - is Brownian Motion and stochastic Flow Systems by Michael Harrison.

In recent times the theory of martingales has become indispensable in probability theory. Do not get a book that does not treat them and illustrate how they are used.

dvchench

This may or may not coincide with the intention of the OP, but I'd like to specify what I'm looking for, since this thread is a prominent google results but does not have much information in terms of answers.

I am a first-year MS student in electrical engineering, doing research with a telecom lab. I am looking for a text that would teach one to understand the most fundamental stochastic processes concepts involved in telecom and internetworking... or at least a general introduction to stochastic processes for readers who do not necessarily enjoy math for math's sake but want to know enough to apply it.

Not sure how popular this books is, but an example of a math book i really liked is the 2nd ed. of Boggess & Narcowich "A first Course in Wavelets with Fourier Analysis". It tries to be self-contained, explains the basic background, and explains using words and examples, not formal, jargon-heavy, convoluted strings of equations pulled out of a standard math reference and served to the reader like a dog's breakfast (as I have seen with so many other math-related books). I'd really like something that tries to avoid unnecessary mathematical depth, but obviously not to the extent that say, Horowitz & Hill does (after all, avoiding math in a math book makes no sense).

any suggestions are much appreciated.

TL;DR: please suggest stochastic processes book for (somewhat) math-fearing electrical engineering student in internetworking/telecom who wants to be able to follow research papers.