Classical Potential Theory and Its Probabilistic Counterpart

Authors:

ISBN: 978-1-4612-9738-3 (Print) 978-1-4612-5208-5 (Online)

Table of contents (32 chapters)

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  1. Front Matter

    Pages i-xxv

  2. Classical and Parabolic Potential Theory

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-13

      Introduction to the Mathematical Background of Classical Potential Theory

    3. No Access

      Book Chapter

      Pages 14-34

      Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions

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      Book Chapter

      Pages 35-44

      Infima of Families of Superharmonic Functions

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      Book Chapter

      Pages 45-56

      Potentials on Special Open Sets

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      Book Chapter

      Pages 57-69

      Polar Sets and Their Applications

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      Book Chapter

      Pages 70-84

      The Fundamental Convergence Theorem and the Reduction Operation

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      Book Chapter

      Pages 85-97

      Green Functions

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      Book Chapter

      Pages 98-140

      The Dirichlet Problem for Relative Harmonic Functions

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      Book Chapter

      Pages 141-154

      Lattices and Related Classes of Functions

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      Book Chapter

      Pages 155-165

      The Sweeping Operation

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      Book Chapter

      Pages 166-194

      The Fine Topology

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      Book Chapter

      Pages 195-225

      The Martin Boundary

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      Book Chapter

      Pages 226-255

      Classical Energy and Capacity

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      Book Chapter

      Pages 256-261

      One-Dimensional Potential Theory

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      Book Chapter

      Pages 262-284

      Parabolic Potential Theory: Basic Facts

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      Book Chapter

      Pages 285-294

      Subparabolic, Superparabolic, and Parabolic Functions on a Slab

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      Book Chapter

      Pages 295-328

      Parabolic Potential Theory (Continued)

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      Book Chapter

      Pages 329-362

      The Parabolic Dirichlet Problem, Sweeping, and Exceptional Sets

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      Book Chapter

      Pages 363-383

      The Martin Boundary in the Parabolic Context

  3. Probabilistic Counterpart of Part 1

    1. Front Matter

      Pages 385-385

    2. No Access

      Book Chapter

      Pages 387-412

      Fundamental Concepts of Probability

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