On uniform positivity of transition densities of small noise constrained diffusions

Amarjit Budhiraja (University of North Carolina at Chapel Hill)
Zhen-Qing Chen (University of Washington)


Constrained diffusions in convex polyhedral cones with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter $\varepsilon> 0$, are considered. Using an interior Dirichlet heat kernel lower bound estimate for second order elliptic operators in bounded domains from Zhang (1995), certain uniform in $\varepsilon$ lower bounds on transition densities of such constrained diffusions are established. These lower bounds together with results from Biswas & Budhiraja (2011) give, under additional stability conditions, an exponential leveling property as $\varepsilon \to 0$ for exit times from suitable bounded domains.

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Pages: 1-9

Publication Date: January 9, 2014

DOI: 10.1214/ECP.v19-2967


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