Classical Potential Theory and Its Probabilistic Counterpart /
From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and pap...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
2001.
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| Series: | Classics in mathematics.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- From the contents: Introduction
- Notation and Conventions
- Part I Classical and Parabolic Potential Theory: Introduction to the Mathematical Background of Classical Potential Theory; Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions; Infirma of Families of Suerharmonic Functions; Potentials on Special Open sets; Polar sets and Their Applications; The Fundamental Convergence Theorem and the Reduction Operation; Green Functions; The Dirichlet Problem for Relative Harmonic Functions; Lattices and Related Classes of Functions; The Sweeping Operation, The Fine Topology; The Martin Boundary; Classical Energy and Capacity; One-Dimensional Potential Theory
- ... Part II Probabilistic Counterpart of Part I ...
- Part III Lattices in Classical Potential Theory and Martingale Theory; Brownian Motion and the PWB Method; Brownian Motion on the Martin Space
- Appendixes.