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Nonlocal Characterizations of Stochastic Completeness on Complete Riemannian Manifolds
In this paper, we first prove that the following generalized conservation principle holds on complete Riemannian manifolds: for every \(00\), \[ T_t^{(s)}\mathbf 1+\int_0^t T_τ^{(s)}\mathcal R_s\,dτ=1 \qquad\text{on }M, \] where \(\mathcal R_s\) is the intrinsic killing term measuring
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