確率モデル入門（第８版） Introduction to Probability Models （8TH）

Ross, Sheldon M.

Academic Pr（2002/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 704 p.
• 言語 ENG
• 商品コード 9780125980555
• DDC分類 519.2

基本説明

Includes new examples and exercises in actuarial sciences. Contains compulsory material for Exam 3 of the Society of Actuaries.

Full Description

"Introduction to Probability Models, 8th Edition", continues to introduce and inspire readers to the art of applying probability theory to phenomena in fields such as engineering, computer science, management and actuarial science, the physical and social sciences, and operations research. Now revised and updated, this best-selling book retains its hallmark intuitive, lively writing style, captivating introduction to applications from diverse disciplines, and plentiful exercises and worked-out examples. The 8th Edition includes five new sections and numerous new examples and exercises, many of which focus on strategies applicable in risk industries such as insurance or actuarial work. The five new sections include: Section 3.6.4 presents an elementary approach, using only conditional expectation, for computing the expected time until a sequence of independent and identically distributed random variables produce a specified pattern; Section 3.6.5 derives an identity involving compound Poisson random variables and then uses it to obtain an elegant recursive formula for the probabilities of compound Poisson random variables whose incremental increases are nonnegative and integer valued; Section 5. 4.3 is concerned with a conditional Poisson process, a type of process that is widely applicable in the risk industries; Section 7.10 presents a derivation of and a new characterization for the classical insurance ruin probability; Section 11.8 presents a simulation procedure known as coupling from the past; its use enables one to exactly generate the value of a random variable whose distribution is that of the stationary distribution of a given Markov chain, even in cases where the stationary distribution cannot itself be explicitly determined. Other Academic Press books by Sheldon Ross include: "Simulation 3rd Ed.", ISBN:0-12-598053-1, "Probability Models for Computer Science", ISBN 0-12-598051-5, "Introduction to Probability and Statistics for Engineers and Scientists, 2nd Ed.", ISBN: 0-12-598472-3. This is a classic text by best-selling author. It continues the tradition of expository excellence. It contains compulsory material for Exam 3 of the Society of Actuaries.

Contents

Preface; Introduction to Probability Theory; Random Variables; Conditional Probability and Conditional Expectation; Markov Chains; The Exponential Distribution and the Poisson Process; Continuous-Time Markov Chains; Renewal Theory and Its Applications; Queueing Theory; Reliability Theory; Brownian Motion and Stationary Processes; Simulation; Appendix: Solutions to Starred Exercises; Index