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Ergodic behavior of diffusions with random jumps from the boundary. (English) Zbl 1158.60036

Summary: We consider a diffusion process on \(D\subset \mathbb R^d\), which upon hitting \(\partial D\), is redistributed in \(D\) according to a probability measure depending continuously on its exit point. We prove that the distribution of the process converges exponentially fast to its unique invariant distribution and characterize the exponent as the spectral gap for a differential operator that serves as the generator of the process on a suitable function space.

MSC:

60J60 Diffusion processes
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