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Contents
Preface v
Notation and Conventions xi
Part A: Simple Markovian Models 1
I Markov Chains 3
1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Aspects of Renewal Theory in Discrete Time . . . . . . 7
3 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Limit Theory . . . . . . . . . . . . . . . . . . . . . . . 16
5 Harmonic Functions, Martingales and Test Functions . 20
6 Nonnegative Matrices . . . . . . . . . . . . . . . . . . . 25
7 The Fundamental Matrix, Poisson's Equation
and the CLT . . . . . . . . . . . . . . . . . . . . . . . . 29
8 Foundations of the General Theory of
Markov Processes . . . . . . . . . . . . . . . . . . . . . 32
II Markov Jump Processes 39
1 Basic Structure . . . . . . . . . . . . . . . . . . . . . . 39
2 The Minimal Construction . . . . . . . . . . . . . . . . 41
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