책 이미지
책 정보
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 계산
· ISBN : 9780521470148
· 쪽수 : 492쪽
목차
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.