Stochastic analysis on Riemannian manifolds without boundary has
been well established. However, the analysis for reflecting
diffusion processes and sub-elliptic diffusion processes is far
from complete. This book contains recent advances in this direction
along with new ideas and efficient arguments, which are crucial for
further developments. Many results contained here (for example, the
formula of the curvature using derivatives of the semigroup) are
new among existing monographs even in the case without boundary.
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