文章基本信息

标题：On uniform positivity of transition densities of small noise constrained diffusions
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作者：Budhiraja, Amarjit ; Chen, Zhen-Qing
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2014
卷号：19
页码：1-9
DOI：10.1214/ECP.v19-2967
语种：English
出版社：Electronic Communications in Probability
摘要：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.
关键词：Exponential leveling, reflected diffusions, Dirichlet heat kernel estimates, Skorohod problem, exit time estimates, Friedlin-Wentzell asymptotics.;Reflected Diffusions, Small noise asymptotics