隨機(jī)過程初級(jí)教程

內(nèi)容概要

本書系統(tǒng)論述隨機(jī)過程的基本理論和方法，理論與實(shí)際應(yīng)用并重。書中主要內(nèi)容有：馬爾可夫鏈、連續(xù)時(shí)間馬爾可夫鏈、更新過程、鞅論、布朗運(yùn)動(dòng)、分支過程和平穩(wěn)隨機(jī)過程。本書涉及范圍十分廣泛，含有豐富的背景知識(shí)，深入淺出，不需要測(cè)度論作為預(yù)備知識(shí)。    本書可作為高等學(xué)校本科生和研究生的教材，也可作為工程技術(shù)人員的參考書。

作者簡(jiǎn)介

Samuel Karlin，斯坦福大學(xué)榮休教授，國(guó)際著名的應(yīng)用概率學(xué)家，美國(guó)科學(xué)院院士，數(shù)理統(tǒng)計(jì)學(xué)會(huì)會(huì)士。1987年獲馮·諾伊曼獎(jiǎng)。在生滅過程中計(jì)算平穩(wěn)分布的Karlin-MeGregor定理即以他的名字命名。

書籍目錄

Chapter 1ELEMENTS OF STOCHASTIC PROCESSES 1.  Review of Basic Terminology and Properties of Random Variables and Distribution Functions 2.  Two Simple Examples of Stochastic Processes 3.  Classification of General Stochastic Processes 4.  Defining a Stochastic Process     Elementary Problems              Problems     Notes         ReferencesChapter 2MARKOV CHAINS 1.  Definitions                       2.  Examples of Markov Chains     3.  Transition Probability Matrices of a Markov Chain 4．Classification of States of a Markov Chain 5．Recurrence 6．Examples of Recurrent Markov Chains 7．More On Recurrence    Elementary Problems    Problems    Notes    ReferencesChapter 3THE BASIC LIMIT THEOREM 0F MARKOV CHAINS AND APPLICATl0NS 1．Discrete Renewal Equation 2．Proof of Theorem 1.1 3．Absorption Probabilities 4．Cfiteria for Recurrence 5．A Queuei~g Example 6．Another Queueing Model 7．Random Walk    Elementary Problems    Problems    Notes    RererenceChapter 4CLASSICAL EXAMPLES 0F CONTINUOUS TIME MARKOV CHAINS  1．General Pure Birth Processes and Poisson Processes  2．More about Poisson Processes  3．A Counter Model  4．Birth and Death Processes  5．Differential Equations of Birth and Death Processes  6．Examples of Birth and Death Processes  7．Birth and Death Processes with Absorbing States  8．Finite State Continuous Time Markov Chains     Elementary Problems     Problems     Notes     ReferencesChapter 5RENEWAL PROCESSESChapter 6MARTINGALESChapter 7 BROWNIAN MOTIONChapter 8BRANCHING PROCESSESChapter 9STATIONARY PROCESSESREVIEW OF MATRIX ANALYSISIndex

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