随机建模原理ELEMENTS OF STOCHASTIC MODELLING
点此进入淘宝搜索页搜索分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者： K.A.BOROVKOV 著
出 版 社： Penguin
出版时间： 2003-12-1字数：版次： 1页数： 342印刷时间： 2003/04/01开本：印次：纸张： 胶版纸I S B N ： 9789812383006包装： 精装内容简介
This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. Rigorous proofs are often replaced with sketches of arguments — with indications as to why a particular result holds, and also how it is connected with other results — and illustrated by examples. Wherever possible, the book includes references to more specialised texts containing both proofs and more advanced material related to the topics covered.
目录
Preface
1.Introduction
2.Basics of probability theory
2.1 Probability spaces
2.2 Distributions and integrals
2.3 Conditional probability and independence
2.4 Random variables and their distributions
2.5 Expectations
2.6 Utility functions
2.7 Integral transforms
2.8 Conditional probabilities and expectations
2.9 Limit theorems
2.10 Stochastic processes
2.11 Recommended literature
2.12 Problems
3.Markov chains
3.1 Definitions
3.2 Classification of states
3.3 Further examples
3.4 Limiting behaviour of Markov chains
3.5 Random walks
3.6 Recommended literature
3.7 Problems
4.Markov decision processes
4.1 Finite-stage models
4.2 Discounted dynamic programming
4.3 Further examples
4.4 Recommended literature
4.5 Problems
5.The exponential distribution and Poisson process
5.1 Properties of the exponential distribution
5.2 Poisson process
5.3 PASTA
5.4 Problems
6.Jump Markov processes
6.1 Definitions and basic results
6.2 Inhomogeneous processes
6.3 Birth-and-death processes
6.4 Recommended literature
6.5 Problems
7.Elements of queueing theory
7.1 Definitions and notation
7.2 Exponential queueing systems
7.2.1 M/M/1 systems
7.2.2 M/M/a systems
7.2.3 M/M/a/N systems
7.3 Machine repair problem
7.4 Exponential queueing networks
7.5 Recommended literature
7.6 Problems
8.Elements of renewal theory
8.1 Definitions and notation. Renewal theorems
8.2 Problems
9.Elements of time series
9.1 Stationary sequences
9.2 Linear filters and linear processes
9.3 A general approach to time series modelling
9.4 Forecasting of time series
10.Elements of simulation
Answers to problems
Greek alphabet
Abbreviations
Index
