Stochastic completeness on complete Riemannian manifolds is equivalent to the zero-mean identity for the fractional Laplacian and uniqueness of bounded distributional solutions to fractional elliptic and parabolic equations.
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Nonlocal Characterizations of Stochastic Completeness on Complete Riemannian Manifolds
Stochastic completeness on complete Riemannian manifolds is equivalent to the zero-mean identity for the fractional Laplacian and uniqueness of bounded distributional solutions to fractional elliptic and parabolic equations.