Escrito por Sheldon Ross y Erol Peköz, este texto lo familiariza con temas avanzados en probabilidad mientras mantiene los requisitos matemáticos al mínimo. Los temas cubiertos incluyen la teoría de la medida, los teoremas de los límites, las probabilidades y expectativas acotadas, el método de acoplamiento y de Stein, las martingalas, las cadenas de Markov, la teoría de la renovación y el movimiento browniano.
Breve descrição
Escrito por Sheldon Ross e Erol Peköz, este texto familiariza você com tópicos avançados em probabilidade, mantendo os requisitos matemáticos no mínimo. Os tópicos abordados incluem teoria da medida, teoremas de limite, probabilidades limitadas e expectativas, o método de acoplamento e Stein, martingales, cadeias de Markov, teoria da renovação e movimento browniano.
Full description
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.
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