Positive Harmonic Functions and Diffusion

Zusammenfassung 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. A useful reference for the specialist! and an excellent guide for the graduate student. Inhaltsverzeichnis 1. Existence and uniqueness for diffusion processes; 2. The basic properties of diffusion processes; 3. The spectral theory of elliptic operators on smooth bounded domains; 4. Generalized spectral theory for operators on arbitrary domains; 5. Applications to the one-dimensional case and the radially symmetric multi-dimensional case; 6. Criteria for transience or recurrence and explosion or non-explosion of diffusion processes; 7. Positive harmonic functions and the Martin boundary: general theory; 8. Positive harmonic functions and the Martin boundary: applications to certain classes of operators; 9. Bounded harmonic functions and applications to Brownian motion and the Laplacian on a manifold of non-positive curvature.

Produktdetails

• Autoren: Ross G. Pinsky
• Mitarbeit: Bela Bollobas (Herausgeber), W. Fulton (Herausgeber)
• Verlag: Cambridge University Press ELT
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 12.01.1995
• EAN: 9780521470148
• ISBN: 978-0-521-47014-8
• Seiten: 492
• Serie: Cambridge Studies in Advanced
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik