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

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

2010-07-22

arxiv.org/abs/1007.3900v3

Mathematics

Probability

Corrected typos, minor modifications

Scientific paper

10.1515/FORM.2011.111

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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