Introduction to stochastic processes－Gregory F. Lawler ，经典教材
DJVU文件
Contents
Preface
Preliminaries 1
0.1 Introduction 1
0.2 Linear Differential Equations 1
0.3 Linear Difference Equations 3
0.4 Exercises 6
Finite Markov Chains 7
1.1 Definitions and Examples 7
1.2 Long-Range Behavior and Invariant Probability 11
1.3 Classification of States 15
1.4 Return Times 22
1.5 Transient States 23
1.6 Examples 28
1.7 Exercises 30
Countable Markov Chains 37
2.1 Introduction 37
2.2 Recurrence and Transience 39
2.3 Positive Recurrence and Null Recurrence 43
2.4 Branching Process 45
2.5 Exercises 49
Continuous-Time Markov Chains 53
3.1 Poisson Process 53
3.2 Finite State Space 56
3.3 Birth-and-Death Processes 62
3.4 General Case 68
3.5 Exercises 69
Optimal Stopping 73
4.1 Optimal Stopping of Markov Chains 73
4.2 Optimal Stopping with Cost 78
4.3 Optimal Stopping with Discounting
4.4 Exercises
5 Martingales
5.1 Conditional Expectation
5.2 Definition and Examples
5.3 Optional Sampling Theorem
5.4 Uniform Integrability
5.5 Martingale Convergence Theorem
5.6 Exercises
6 Renewal Processes
6.1 Introduction
6.2 Renewal Equation
6.3 Discrete Renewal Processes
6.4 M/G/l and G/M/l Queues
6.5 Exercises
7 Reversible Markov Chains
7.1 Reversible Processes
7.2 Convergence to Equilibrium
7.3 Markov Chain Algorithms
7.4 A Criterion for Recurrence
7.5 Exercises
8 Brownian Motion
8.1 Introduction
8.2 Markov Property
8.3 Zero Set of Brownian Motion
8.4 Brownian Motion in Several Dimensions
8.5 Recurrence and Transience
8.6 Fractal Nature of Brownian Motion
8.7 Brownian Motion with Drift
8.8 Exercises
9 Stochastic Integration
9.1 Integration with Respect to Random Walk
9.2 Integration with Respect to Brownian Motio
9.3 Ito's Formula
9.4 Simulation
9.5 Exercises
Index