確率の応用（テキスト）<br>Applied Probability (Springer Texts in Statistics) （Corr. repr. 2005. XII, 300 p. w. figs. 24,5 cm）

確率の応用（テキスト）
Applied Probability (Springer Texts in Statistics) （Corr. repr. 2005. XII, 300 p. w. figs. 24,5 cm）

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  • 製本 Hardcover:ハードカバー版／ページ数 320 p.
  • 商品コード 9780387004259

基本説明

Presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences.

Full Description


This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, "Applied Probability" presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes.If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material here for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. Finally, Chapters 12 and 13 develop the Chen-Stein method of Poisson approximation and connections between probability and number theory. Kenneth Lange is Professor of Biomathematics and Human Genetics and Chair of the Department of Human Genetics at the UCLA School of Medicine. He has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer-Verlag published his books "Numerical Analysis for Statisticians" and "Mathematical and Statistical Methods for Genetic Analysis Second Edition", in 1999 and 2002, respectively.

Contents

Basic Notions of Probability Theory * Calculation of Expectations * Convexity, Optimization, and Inequalities * Combinatorics * Combinatorial Optimization * Poisson Processes * Discrete-Time Markov Chains * Continuous-Time Markov Chains * Branching Processes * Martingales * Diffusion Processes * Poisson Approximation * Number Theory