A Second Course in Probability
By S. Ross, Erol A. Peköz. 2007
83 citations recorded by the source corpus.
Written by Sheldon Ross and Erol Peköz, this text familiarises you with advanced topics in probability while keeping the mathematical prerequisites to a minimum. Topics covered include measure theory, limit theorems, bounding probabilities and expectations, coupling and Stein's method, martingales, Markov chains, renewal theory, and Brownian motion. No other text covers all these topics rigorously but at such an accessible level - all you need is an undergraduate-level understanding of calculus and probability. New to this edition are sections on the gambler's ruin problem, Stein's method as applied to exponential approximations, and applications of the martingale stopping theorem. Extra end-of-chapter exercises have also been added, with selected solutions available.This is an ideal textbook for students taking an advanced undergraduate or graduate course in probability. It also represents a useful resource for professionals in relevant application domains, from finance to machine learning.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/385eb51e12a3c2707a3360de60781e3108ab32f9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Statistics and Probability
- Nathan Ross
- C. Burges
- Jim G. Dai
- Anton Braverman
- Per-Gunnar Martinsson
- Joel A. Tropp
- C. Houdr'e
- B. Arras
Citations in the corpus
- Vox Populi: Collecting High-Quality Labels from a Crowd (2009, unknown): “8 in [RP07]), which implies that ∑ n |Pr(|St| = n|)−Pr(N = n)| ≤ m/k(2).”
- Fundamentals of Stein's method (2011, background): “A similar undertaking but with smaller scope can be found in Chapter 2 of [51], which also serves as a nice introduction to the basics of Stein’s method.”
- Dimension Reduction: A Guided Tour (2010, background): “By the tower property [Ross and Peköz, 2007], and by conditional independence, E[X|Y ] = E[E[X|{aiX}, Y ]|Y ] = E[E[X|{aiX}]|Y ], so by linearity of expectation, for any s in the space orthogonal to the ΣXXai, we have that s ′E[X|Y ] = E[E[s′X|{aiX}]|Y ] = 0.”