Electronic Communications in Probability

On uniform positivity of transition densities of small noise constrained diffusions

Amarjit Budhiraja and Zhen-Qing Chen

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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.

Article information

Electron. Commun. Probab., Volume 19 (2014), paper no. 1, 9 pp.

Accepted: 9 January 2014
First available in Project Euclid: 7 June 2016

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Primary: Reflected Diffusions
Secondary: Small noise asymptotics

Exponential leveling reflected diffusions Dirichlet heat kernel estimates Skorohod problem exit time estimates Friedlin-Wentzell asymptotics

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Budhiraja, Amarjit; Chen, Zhen-Qing. On uniform positivity of transition densities of small noise constrained diffusions. Electron. Commun. Probab. 19 (2014), paper no. 1, 9 pp. doi:10.1214/ECP.v19-2967. https://projecteuclid.org/euclid.ecp/1465316703

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