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Classical Potential Theory and Its Probabilistic Counterpart

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Cover of 'Classical Potential Theory and Its Probabilistic Counterpart'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction to the Mathematical Background of Classical Potential Theory
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    Chapter 2 Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions
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    Chapter 3 Infima of Families of Superharmonic Functions
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    Chapter 4 Potentials on Special Open Sets
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    Chapter 5 Polar Sets and Their Applications
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    Chapter 6 The Fundamental Convergence Theorem and the Reduction Operation
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    Chapter 7 Green Functions
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    Chapter 8 The Dirichlet Problem for Relative Harmonic Functions
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    Chapter 9 Lattices and Related Classes of Functions
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    Chapter 10 The Sweeping Operation
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    Chapter 11 The Fine Topology
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    Chapter 12 The Martin Boundary
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    Chapter 13 Classical Energy and Capacity
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    Chapter 14 One-Dimensional Potential Theory
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    Chapter 15 Parabolic Potential Theory: Basic Facts
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    Chapter 16 Subparabolic, Superparabolic, and Parabolic Functions on a Slab
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    Chapter 17 Parabolic Potential Theory (Continued)
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    Chapter 18 The Parabolic Dirichlet Problem, Sweeping, and Exceptional Sets
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    Chapter 19 The Martin Boundary in the Parabolic Context
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    Chapter 20 Fundamental Concepts of Probability
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    Chapter 21 Optional Times and Associated Concepts
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    Chapter 22 Elements of Martingale Theory
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    Chapter 23 Basic Properties of Continuous Parameter Supermartingales
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    Chapter 24 Lattices and Related Classes of Stochastic Processes
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    Chapter 25 Markov Processes
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    Chapter 26 Brownian Motion
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    Chapter 27 The Itô Integral
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    Chapter 28 Brownian Motion and Martingale Theory
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    Chapter 29 Conditional Brownian Motion
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    Chapter 30 Lattices in Classical Potential Theory and Martingale Theory
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    Chapter 31 Brownian Motion and the PWB Method
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    Chapter 32 Brownian Motion on the Martin Space
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Title
Classical Potential Theory and Its Probabilistic Counterpart
Published by
Springer-Verlag Berlin Heidelberg, January 2001
DOI 10.1007/978-3-642-56573-1
ISBNs
978-3-64-256573-1, 978-3-54-041206-9
Authors

Joseph L. Doob, Doob, Joseph L.

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