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Stochastic representation of reflecting diffusions corresponding to divergence form operators. (English) Zbl 0979.60069

Summary: We obtain a stochastic representation of a diffusion corresponding to a uniformly elliptic divergence form operator with co-normal reflection at the boundary of a bounded \(C^2\)-domain. We also show that the diffusion is a Dirichlet process for each starting point inside the domain.

MSC:

60J60 Diffusion processes
35K20 Initial-boundary value problems for second-order parabolic equations
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