Applied Probability

Kenneth Lange

312 pages, parution le 14/04/2003

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Résumé

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.

L'auteur - Kenneth Lange

UCLA School of Medicine, Los Angeles, CA, USA

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Kenneth Lange
Parution	14/04/2003
Nb. de pages	312
Format	16 x 24
Couverture	Relié
Poids	590g
Intérieur	Noir et Blanc
EAN13	9780387004259
ISBN13	978-0-387-00425-9