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Krylov-Safonov estimates for a degenerate diffusion process. (English) Zbl 1451.60094

Summary: This paper proves a Krylov-Safonov estimate for a multidimensional diffusion process whose diffusion coefficients are degenerate on the boundary. As applications the existence and uniqueness of invariant probability measures for the process and Hölder estimates for the associated partial differential equation are obtained.

MSC:

60J60 Diffusion processes
60K50 Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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