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

Masayoshi Takeda; Gerald Trutnau

doi:10.1515/form.2011.111

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arXiv · 1007.3900

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

Masayoshi Takeda·Gerald Trutnau

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Abstract

Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general perturbed divergence form operators. Our main tool is a recently extended forward and backward martingale decomposition, which reduces to the well-known Lyons-Zheng decomposition in the symmetric case.

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Masayoshi Takeda, Gerald Trutnau. 2011-03-24. Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms. https://doi.org/10.1515/form.2011.111

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