Probability Theory Referance
 

I'm looking for a book that goes through probability theory in a rigorous/measure-theoretic manner. Specifically, I'd prefer something that goes through stochastic calculus/pde's, brownian motion, and markov chains.

Anyone have any good references they can recommend?

Re: Probability Theory Referance
 

[ QUOTE ]
I'm looking for a book that goes through probability theory in a rigorous/measure-theoretic manner. Specifically, I'd prefer something that goes through stochastic calculus/pde's, brownian motion, and markov chains.

Anyone have any good references they can recommend?

[/ QUOTE ]

Probability, Random Variables, and Stochastic Processes by Papoulis is a classic text that has these topics and contains some rigor. My grad level EE probability courses used it, and it is full of great examples, though many are EE related. If you completely understood every example from just 1 chapter you would really have something.

The 2 volume set by Feller is another classic for probability theory and contains many advanced topics, though not necessarily heavy on measure theory.

Re: Probability Theory Referance
 

Probability: Theory and Examples (3rd Edition) by Richard Durrett is decent.

SDE
 

I don't know about the quality of it, but you can't argue with the price.

math.berkeley.edu/~evans/SDE.course.pdf

Re: SDE
 

[ QUOTE ]
I don't know about the quality of it, but you can't argue with the price.

math.berkeley.edu/~evans/SDE.course.pdf

[/ QUOTE ]

I don't know this book but Evans' book on Partial Differential Equations is the standard introductory graduate text now.

Re: SDE
 

[ QUOTE ]
I don't know about the quality of it, but you can't argue with the price.

math.berkeley.edu/~evans/SDE.course.pdf

[/ QUOTE ]

Meet all your requirements, I think.
[I'm looking for a book that goes through probability theory in a rigorous/measure-theoretic manner. Specifically, I'd prefer something that goes through stochastic calculus/pde's, brownian motion, and markov chain]

Re: SDE
 

[ QUOTE ]
I don't know about the quality of it, but you can't argue with the price.

math.berkeley.edu/~evans/SDE.course.pdf

[/ QUOTE ]

given the author and the fact that this seems to cover what I was looking for and that it's conviently located online, I suppose I'll start with this and investigate Jason and Bruce's suggestions if the need arises.

Thanks a lot guys.