滿額折
從馬爾科夫鏈到非平衡粒子系統(第2版)（簡體書）
商品資訊
ISBN13：9787510068232
出版社：世界圖書(北京)出版公司
作者：陳木法
出版日：2014/02/26
裝訂／頁數：平裝／624頁
商品簡介
目次
商品簡介
Themainpurposeofthebookistointroducesomeprogressonprobabilitytheoryanditsapplicationstophysics，madebyChineseprobabilists，especiallybyagroupatBeijingNormalUniversityinthepast15years.Uptonow，mostoftheworkisonlyavailablefortheChinese-speakingpeople.Inordertomakethebookasself-containedaspossibleandsuitableforawiderrangeofreaders，afundamentalpartofthesubject，contributedbymanymathematiciansfromdifferentcountries，isalsoincluded.Thebookstartswithsomenewcontributionstotheclassicalsubject-Markovchains，thengoestothegeneraljumpprocessesandsymmetrizablejumpprocesses，equilibriumparticlesystemsandnon-equilibriumparticlesystems.Accordinglythebookisdividedintofourparts.AnelementaryoverlookofthebookispresentedinChapter0.Somenotesonthebibliographiesandopenproblemsarecollectedinthelastsectionofeachchapter.Itishopedthatthebookcouldbeusefulforbothexpertsandnewcomers，notonlyformathematiciansbutalsofortheresear本書主要闡述概率論及其在物理學中的應用全書分為4部分，16章。作者陳木法是北京師範大學教授，中科院院士。本書可作為隨機過程課程研究生教材。111111111111111111111111111111111111111111111111111111111111111111111111
目次
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
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
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