Advanced probability book recommendation

Question

I am looking for an advanced probability book to discover more advanced topics ( central limits for stochastic process, sde, MC...). I have read a couple of chapters in each of the standard graduate probability books (durrett, williams, kallenberg)

Answer 1

If you like your books to be really advanced, my personal favorite is:

Probability with a View Towards Statistics by Lucien M. Le Cam

It is quite advanced and you'll find a lot of modern material (sde, CLT for stochastic process, MC, ...) in there. For a more classical approach, my favorite is:

Introduction to Probability and Measure by Billingsley

Answer 2

I strongly recommend Measure Theory and Probability Theory by Krishna B. Athreya and Soumendra N. Lahiri. If you are interested in Mathematical Statistics, I would recommend the book Mathematical Statistics from Jun Shao, which is very mathematically flavored.