On Uniform Positivity of Transition Densities of Small Noise Constrained Diffusions

2013/08/16 by Amarjit Budhiraja, Zhen-Qing Chen, Budhiraja, Amarjit +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1308.3533

arxiv created 2013/08/16 · arxiv updated 2013/08/19

Abstract

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for second order elliptic operators in bounded domains from [13], certain uniform in the scaling parameter 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 the scaling parameter approaches zero, for exit times from suitable bounded domains.

Related

• Bounds for the gradient of the transition kernel for elliptic operators with unbounded diffusion, drift and potential term
• Pathwise differentiability of reflected diffusions in convex polyhedral domains
• On low frequency inference for diffusions without the hot spots conjecture
• A Monte Carlo method for estimating sensitivities of reflected diffusions in convex polyhedral domains
• Heat kernel for reflected diffusion and extension property on uniform domains