Positive harmonic functions and diffusion
Series: Cambridge studies in advanced mathematics ; 45Publication details: Cambridge University Press, 1995. Cambridge:Description: xvi, 474 p. ; pb, 24 cmISBN:- 9780521059831
- 519.233 PIN
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
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Books | IIT Gandhinagar General Stacks | General | 519.233 PIN (Browse shelf(Opens below)) | 1 | Available | 030147 |
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519.233 KAL Stochastic analysis and diffusion processes | 519.233 KAL Stochastic analysis and diffusion processes | 519.233 MAR Markov processes, Gaussian processes, and local times | 519.233 PIN Positive harmonic functions and diffusion | 519.233 PRI Understanding markov chains: examples and applications | 519.233 YIN Hybrid switching diffusions: properties and applications | 519.24 HOS Regional frequency analysis: an approach based on L-moments |
Includes bibliographical references ([461]-470) and index.
In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.
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