Krylov-Safonov estimates for a degenerate diffusion process
Fu Zhang, Kai Du
TL;DR
This paper establishes Krylov-Safonov estimates for a multidimensional degenerate diffusion process, leading to results on invariant measures and Hölder regularity for related PDEs.
Contribution
It provides the first Krylov-Safonov estimate for degenerate boundary diffusion processes, enabling new existence, uniqueness, and regularity results.
Findings
Existence of invariant probability measures.
Uniqueness of invariant measures.
Hölder estimates for associated PDEs.
Abstract
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 Hoelder estimates for the associated partial differential equation are obtained.
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Taxonomy
TopicsStochastic processes and financial applications · Advanced Mathematical Modeling in Engineering · Stability and Controllability of Differential Equations