Measure-Theoretic Probability
With Applications to Statistics, Finance, and Engineering
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Beschreibung
This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more.
Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study. Prerequisites include a basic knowledge of probability and elementary concepts from real analysis.This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more.
Measure-Theoretic Probability is ideal for a one-semester course and will best suit undergraduates studying statistics, data science, financial engineering, and economics who want to understand and apply more advanced ideas from probability to their disciplines. As a concise and rigorous introduction to measure-theoretic probability, it is also suitable for self-study.Prerequisites include a basic knowledge of probability and elementary concepts from real analysis.
Provides an accessible introduction to measure-theoretic probability for undergraduate students Appeals to a broad audience of undergraduates with informative examples from statistics and engineering Demonstrates how probability is used in a variety of exciting fields, with interesting applications appearing throughout
Autor*in
Kenneth Shum
Themen in »Measure-Theoretic Probability«
Probability theory Measure theory Probability applications Real analysis Measure-theoretic probability Riemann-Stieltjes integral Sigma fields Random variables Statistical independence Borel-Cantelli lemmas Lebesgue integral Optimal transport problem Convergence modes Hilbert space theory Levy's continuity theorem