Positive Harmonic Functions and Diffusion

ISBN: 9780521059831 出版年：1995 页码：492 Ross G Pinsky Cambridge University Press

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.