Description This lively introduction to measure-theoretic probability Theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion.
The new edition re-instates discussion about the central limit theorem for martingales and stationary sequences..
Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas.
Setting the foundation for this expansion, Chapter 7 now features a proof of It \'s formula.
This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), an advanced topic that is finding new applications.
Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended Examples that apply the Theory to concrete applications.
Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference.
Description This lively introduction to measure-theoretic probability Theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion
