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On uniform positivity of transition densities of small noise constrained diffusions

   
@article{ECP2967,
	author = {Amarjit Budhiraja and Zhen-Qing Chen},
	title = {On uniform positivity of transition densities of small noise constrained diffusions},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {Exponential leveling, reflected diffusions, Dirichlet heat kernel estimates, Skorohod problem, exit time estimates, Friedlin-Wentzell asymptotics.},
	abstract = {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.},
	pages = {no. 1, 1-9},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-2967},    
        url = {http://ecp.ejpecp.org/article/view/2967}}