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Let E be an unbounded open (or closed) domain in Euclidean space of dimensiongreater or equal to two. We present conservativeness criteria for (possiblyreflected) diffusions with state space E that are associated to fairly generalperturbed divergence form operators. Our main tool is a recently extendedforward and backward martingale decomposition, which reduces to the well-knownLyons-Zheng decomposition in the symmetric case.

Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms