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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) Book

Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)
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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35), This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elemen, Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)
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  • Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)
  • Written by author Zhen-Qing Chen
  • Published by Princeton University Press, 11/20/2011
  • This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elemen
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Notation ix

Preface xi

Chapter 1 Symmetric Markovian Semigroups and Dirichlet Forms 1

1.1 Dirichlet Forms and Extended Dirichlet Spaces 1

1.2 Excessive Functions and Capacities 15

1.3 Quasi-Regular Dirichlet Forms 24

1.4 Quasi-Homeomorphism of Dirichlet Spaces 30

1.5 Symmetric Right Processes and Quasi-Regular Dirichlet Forms 33

Chapter 2 Basic Properties and Examples of Dirichlet Forms 37

2.1 Transience, Recurrence, and Irreducibility 37

2.2 Basic Examples 50

2.3 Analytic Potential Theory for Regular Dirichlet Forms 77

2.4 Local Properties 88

Chapter 3 Symmeteic Hunt Processes and Rrgular Dirichlet Forms 92

3.1 Relations between Probabilistic and Analytic Concepts 92

3.2 Hitting Distributions and Projections I 103

3.3 Quasi Properties, Fine Properties, and Part Processes 106

3.4 Hitting Distributions and Projections II 113

3.5 Transience, Recurrence, and Path Behavior 118

Chapter 4 Additive Functional of Symmetric Merkov Processes 130

4.1 Positive Continuous Additive Functionals and Smooth Measures 130

4.2 Decompositions of Additive Functionals of Finite Energy 143

4.3 Probabilistic Derivation of Beurling-Deny Formula 151

Chapter 5 Time Changes of Symmetrix Markov Processes 166

5.1 Subprocesses and Perturbed Dirichlet Forms 168

5.2 Time Changes and Trace Dirichlet Forms 174

5.3 Examples 190

5.4 Energy Functional for Transient Processes 202

5.5 Trace Dirichlet Forms and Feller Measures 206

5.6 Characterization of Time-Changed Processes 221

5.7 Excursions, Exit System, and Feller Measures 225

5.8 More Examples 232

Chapter 6 Rrflected Dirichlet Spaces 240

6.1 Terminal Random Variables and Harmonic Functions 241

6.2 Reflected Dirichlet Spaces: Transient Case 246

6.3 Recurrent Case 260

6.4 Toward Quasi-Regular Cases 262

6.5 Examples 269

6.6 Silverstein Extensions 275

6.7 Equivalent Notions of Harmonicity 263

Chapter 7 Boundary Theory for Symmetric Markov Processes 300

7.1 Reflected Dirichlet Space for Part Processes 302

7.2 Douglas Integrals and Reflecting Extensions 310

7.3 Lateral Condition for L2-Generator 324

7.4 Countable Boundary 334

7.5 One-Point Extensions 340

7.6 Examples of One-Point Extensions 352

7.7 Many-Point Extensions 369

7.8 Examples of Many-Point Extensions 377

Appendix A Essentials of Markov Processes 391

A.1 Markov Processes 391

A.2 Basic Properties of Borel Right Processes 413

A.3 Additive Functionals of Right Processes 423

A.4 Review of Symmetric Forms 440

Appendix B Solutions to Exercises 443

Notes 451

Bibliography 457

Catalogue of Some Useful Theorems 467

Index 473


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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35), This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elemen, Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35), This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elemen, Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35), This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elemen, Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

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