![A Basic Course in Probability Theory (2nd edition) [Repost]](https://pixhost.icu/avaxhome/41/fd/004cfd41_medium.jpg)
A Basic Course in Probability Theory (2nd edition) [Repost]
![A Basic Course in Probability Theory (2nd edition) [Repost]](https://pixhost.icu/avaxhome/41/fd/004cfd41.jpg)
Rabi Bhattacharya, Edward C. Waymire - A Basic Course in Probability Theory (2nd edition)
Published: 2017-02-16 | ISBN: 3319479725 | PDF | 265 pages | 3.41 MB
This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem.