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| Titre : | Positive harmonic functions and diffusion : An integrated analytic and probabilistic approach | | Type de document : | texte imprimé | | Auteurs : | Ross Pinsky, Auteur | | Editeur : | Cambridge [United Kingdom] : Cambridge University Press | | Année de publication : | 1995 | | Collection : | Cambridge studies in advanced mathematics | | Importance : | XVI- 474p. | | Format : | 24cm. | | ISBN/ISSN/EAN : | 978-0-521-47014-8 | | Langues : | Anglais | | Catégories : | MATH:515 Analyse
| | Mots-clés : | Diffusion processes Elliptic operators | | Résumé : | In this book, Professor Pinsky gives a self-contained account of the construction and basic properties of diffusion processes, including both analytic and probabilistic techniques. He starts with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, and then develops the theory of the generalized principal eigenvalue and the related criticality theory for elliptic operators on arbitrary domains. He considers Martin boundary theory and calculates the Martin boundary 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 a manifold. Many results that form the folklore of the subject are given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student. |
Positive harmonic functions and diffusion : An integrated analytic and probabilistic approach [texte imprimé] / Ross Pinsky, Auteur . - Cambridge (United Kingdom) : Cambridge University Press, 1995 . - XVI- 474p. ; 24cm.. - ( Cambridge studies in advanced mathematics) . ISBN : 978-0-521-47014-8 Langues : Anglais | Catégories : | MATH:515 Analyse
| | Mots-clés : | Diffusion processes Elliptic operators | | Résumé : | In this book, Professor Pinsky gives a self-contained account of the construction and basic properties of diffusion processes, including both analytic and probabilistic techniques. He starts with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, and then develops the theory of the generalized principal eigenvalue and the related criticality theory for elliptic operators on arbitrary domains. He considers Martin boundary theory and calculates the Martin boundary 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 a manifold. Many results that form the folklore of the subject are 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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