Epub mathematics of probability epub

This book covers the basics of modern probability theory It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory which is followed by some initial applications to probability theory including independence and conditional expectations The second half of the book deals with Gaussian random variables with Markov chains with a few continuous parameter processes including Brownian motion and finally with martingales both discrete and continuous parameter ones The book is a self contained introduction to probability theory and the measure theory required to study it Mathematics of Probability Graduate Studies in Mathematics Graduate Studies in Mathematics 149 A very good book for first year statistics PhD students who want a rigorous foundation in probability theory Hardcover