杰克德编著的《随机过程用的极限定理（第2版）》的第一版成为学习随机过程函数收敛的必备读物，这部科学巨着终于出第2版了，仍然延续了第1版的风格，但增加了不少新的知识，在厚度上的增加了将近50面。第1版面世后，可预测的一致胎紧性有了很大的进展，所以书中也做了全面的更新。本书仍然是学习随机过程的一本不可或缺的参考书。目次：随机过程一般概念；半鞅和独立增量过程的特征；鞅问题和测量改变；Hellinger过程、绝对连续和测度奇异性；绝对连续和奇异的可预测准则；近邻性、完全独立和变分收敛；Skorokhod拓扑和过程收敛；具有独立增量的过。

Chapter Ⅰ The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals

1.Stochastic Basis, Stopping Times, Optional a -Field, Martingales

a.Stochastic Basis

b.Stopping Times

c.The Optional σ-Field

d.The Localization Procedure

e.Martingales

f.The Discrete Case

2.Predictable σ-Field, Predictable Times

a.The Predictable σ-Field

b.Predictable Times

c.Totally Inaccessible Stopping Times

d.Predictable Projection

e.The Discrete Case

3.Increasing Processes

a.Basic Properties

b.Doob-Meyer Decomposition and Compensators of Increasing Processes

c.Lenglart Domination Property

d.The Discrete Case

4.Semimartingales and Stochastic Integrals

a.Locally Square-Integrable Martingales

b.Decompositions of a Local Martingale

c.Semimartingales

d.Construction of the Stochastic Integral

e.Quadratic Variation of a Semimartingale and Ito's Formula

f.Doleans-Dade Exponential Formula

g.The Discrete Case

Chapter Ⅱ Characteristics of Semimartingales and Processes with Independent Increments

1.Random Measures

1a.General Random Measures

1b.Integer-Valued Random Measures

1c.A Fundamental Example: Poisson Measures

1d.Stochastic Integral with Respect to a Random Measure

2.Characteristics of Semimartingales

2a.Definition of the Characteristics

2b.Integrability and Characteristics

2c.A Canonical Representation for Semimartingales

2d.Characteristics and Exponential Formula

3.Some Examples

3a.The Discrete Case

3b.More on the Discrete Case

3c.The "One-Point" Point Process and Empirical Processes

4.Semimartingales with Independent Increments

4a.Wiener Processes

4b.Poisson Processes and Poisson Random Measures

4c.Processes with Independent Increments and Semimartingales

4d.Gaussian Martingales

5.Processes with Independent Increments Which Are Not Semimartingales

5a.The Results

5b.The Proofs

6.Processes with Conditionally Independent Increments

7.Progressive Conditional Continuous PIIs

8.Semimartingales, Stochastic Exponential and Stochastic Logarithm

8a.More About Stochastic Exponential and Stochastic Logarithm,

8b.Multiplicative Decompositions and Exponentially Special Semimartingales

Chapter Ⅲ Martingale Problems and Changes of Measures

1.Martingale Problems and Point Processes

1a.General Martingale Problems

1b.Martingale Problems and Random Measures

1c.Point Processes and Multivariate Point Processes

……

Chapter Ⅳ Bellinger Processes, Absolute Continuity

Chapter Ⅴ Contiguity, Entire Separation, Convergence in Variation

Chapter Ⅵ Skorokhod Topology and Convergence of Processes

Chapter Ⅶ Convergence of Processes with Independent Increments

Chapter Ⅷ Convergence to a Process with Independent Increments

Chapter Ⅸ Convergence to a Semimartingale

Chapter Ⅹ Limit Theorems, Density Processes and Contiguity Bibliographical Comments

References

Index of Symbols

Index of Terminology

Index of Topics

Index of Conditions for Limit Theorems