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从马尔科夫链到非平衡料子系统 第2版（英文影印版）
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从马尔科夫链到非平衡料子系统 第2版（英文影印版）
出版时间：2014年版
内容简介
The main purpose of the book is to introduce some progress on probability theory and its applications to physics， made by Chinese probabilists，especially by a group at Beijing Normal University in the past 15 years. Up to now， most of the work is only available for the Chinese-speaking people.In order to make the book as self-contained as possible and suitable for a wider range of readers， a fundamental part of the subject， contributed by many mathematicians from different countries， is also included. The book starts with some new contributions to the classical subject-Markov chains，then goes to the general jump processes and symmetrizable jump processes，equilibrium particle systems and non-equilibrium particle systems. Accordingly the book is divided into four parts.An elementary overlook of the book is presented in Chapter 0. Some notes on the bibliographies and openproblems are collected in the last section of each chapter. It is hoped that the book could be useful for both experts and newcomers， not only for mathematicians but also for the researchers in related areas such as mathematicalphysics， chemistry and biology.
目录
Preface to the First Edition
Preface to the Second Edition
Chapter 0. An Overview of the Book:
Starting From Markov Chains
0.1. Three Classical Problems for Markov Chains
0.2. Probability Metrics and Coupling Methods
0.3. Reversible Markov Chains
0.4. Large Deviations and Spectral Gap
0.5. Equilibrium Particle Systems
0.6. Non-equilibrium Particle Systems
Part I. General Jump Processes
Chapter 1. Transition Function and its Laplace Transform
1.1. Basic Properties of Transition Function
1.2. The q-Pair
1.3. Differentiability
1.4. Laplace Transforms
1.5. Appendix
1.6. Notes
Chapter 2. Existence and Simple Constructions of Jump Processes
2.1. Minimal Nonnegative Solutions
2.2. Kolmogorov Equations and Minimal Jump Process
2.3. Some Sufficient Conditions for Uniqueness
2.4. Kolmogorov Equations and q-Condition
2.5. Entrance Space and Exit Space
2.6. Construction of q-Processes with Single-Exit q-Pair
2.7. Notes
Chapter 3. Uniqueness Criteria
3.1. Uniqueness Criteria Based on Kolmogorov Equations
3.2. Uniqueness Criterion and Applications
3.3. Some Lemmas
3.4. ProofofUniqueness Criterion
3.5. Notes
Chapter 4. Recurrence, Ergodicity and Invariant Measures
4.1. Weak Convergence
4.2. General Results
4.3. Markov Chains: Time-discrete Case
4.4. Markov Chains: Time-continuous Case
4.5. Single Birth Processes
4.6. Invariant Measures
4.7. Notes
Chapter 5. Probability Metrics and Coupling Methods
5.1. Minimum Lp-Metric
5.2. Marginality and Regularity
5.3. Successful Coupling and Ergodicity
5.4. OptimalMarkovian Couplings
5.5. Monotonicity
5.6. Examples
5.7 Notes
Part II. Symmetrizable Jump Processes
Chapter 6. Symmetrizable Jump Processes and Dirichlet Forms ,
6.1. Reversible Markov Processes
6.2. Existence
6.3. Equivalence of Backward and Forward Kolmogorov Equations
6.4. General Representation of Jump Processes
6.5. Existence of Honest Reversible Jump Processes
6.6. Uniqueness Criteria
6.7. Basic Dirichlet Form
6.8. Regularity, Extension and Uniqueness
6.9. Notes
Chapter 7. Field Theory
7.1. Field Theory
7.2. Lattice Field
7.3. Electric Field
7.4. Transience of Symmetrizable Markov Chains
7.5. Random Walk on Lattice Fractals
7.6. A Comparison Theorem
7.7. Notes
……
Part III. Equilibrium Particle Systems
Part Ⅳ. Non-equilibrium Particle
Systems
出版时间：2014年版
内容简介
The main purpose of the book is to introduce some progress on probability theory and its applications to physics， made by Chinese probabilists，especially by a group at Beijing Normal University in the past 15 years. Up to now， most of the work is only available for the Chinese-speaking people.In order to make the book as self-contained as possible and suitable for a wider range of readers， a fundamental part of the subject， contributed by many mathematicians from different countries， is also included. The book starts with some new contributions to the classical subject-Markov chains，then goes to the general jump processes and symmetrizable jump processes，equilibrium particle systems and non-equilibrium particle systems. Accordingly the book is divided into four parts.An elementary overlook of the book is presented in Chapter 0. Some notes on the bibliographies and openproblems are collected in the last section of each chapter. It is hoped that the book could be useful for both experts and newcomers， not only for mathematicians but also for the researchers in related areas such as mathematicalphysics， chemistry and biology.
目录
Preface to the First Edition
Preface to the Second Edition
Chapter 0. An Overview of the Book:
Starting From Markov Chains
0.1. Three Classical Problems for Markov Chains
0.2. Probability Metrics and Coupling Methods
0.3. Reversible Markov Chains
0.4. Large Deviations and Spectral Gap
0.5. Equilibrium Particle Systems
0.6. Non-equilibrium Particle Systems
Part I. General Jump Processes
Chapter 1. Transition Function and its Laplace Transform
1.1. Basic Properties of Transition Function
1.2. The q-Pair
1.3. Differentiability
1.4. Laplace Transforms
1.5. Appendix
1.6. Notes
Chapter 2. Existence and Simple Constructions of Jump Processes
2.1. Minimal Nonnegative Solutions
2.2. Kolmogorov Equations and Minimal Jump Process
2.3. Some Sufficient Conditions for Uniqueness
2.4. Kolmogorov Equations and q-Condition
2.5. Entrance Space and Exit Space
2.6. Construction of q-Processes with Single-Exit q-Pair
2.7. Notes
Chapter 3. Uniqueness Criteria
3.1. Uniqueness Criteria Based on Kolmogorov Equations
3.2. Uniqueness Criterion and Applications
3.3. Some Lemmas
3.4. ProofofUniqueness Criterion
3.5. Notes
Chapter 4. Recurrence, Ergodicity and Invariant Measures
4.1. Weak Convergence
4.2. General Results
4.3. Markov Chains: Time-discrete Case
4.4. Markov Chains: Time-continuous Case
4.5. Single Birth Processes
4.6. Invariant Measures
4.7. Notes
Chapter 5. Probability Metrics and Coupling Methods
5.1. Minimum Lp-Metric
5.2. Marginality and Regularity
5.3. Successful Coupling and Ergodicity
5.4. OptimalMarkovian Couplings
5.5. Monotonicity
5.6. Examples
5.7 Notes
Part II. Symmetrizable Jump Processes
Chapter 6. Symmetrizable Jump Processes and Dirichlet Forms ,
6.1. Reversible Markov Processes
6.2. Existence
6.3. Equivalence of Backward and Forward Kolmogorov Equations
6.4. General Representation of Jump Processes
6.5. Existence of Honest Reversible Jump Processes
6.6. Uniqueness Criteria
6.7. Basic Dirichlet Form
6.8. Regularity, Extension and Uniqueness
6.9. Notes
Chapter 7. Field Theory
7.1. Field Theory
7.2. Lattice Field
7.3. Electric Field
7.4. Transience of Symmetrizable Markov Chains
7.5. Random Walk on Lattice Fractals
7.6. A Comparison Theorem
7.7. Notes
……
Part III. Equilibrium Particle Systems
Part Ⅳ. Non-equilibrium Particle
Systems
