On Uniform Positivity of Transition Densities of Small Noise Constrained Diffusions
نویسنده
چکیده
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter ε > 0, are considered. Using an interior Dirichlet heat kernel lower bound estimate for second order elliptic operators in bounded domains from [13], certain uniform in ε lower bounds on transition densities of such constrained diffusions are established. These lower bounds together with results from [1] give, under additional stability conditions, an exponential leveling property as ε → 0 for exit times from suitable bounded domains. AMS 2000 subject classifications: Primary 60F10, 60J60, 60J25; secondary 93E15, 90B15.
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