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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316703

Digital Object Identifier
doi:10.1214/ECP.v19-2967

Mathematical Reviews number (MathSciNet)
MR3164748

Zentralblatt MATH identifier
1329.60276

Subjects
Primary: Reflected Diffusions
Secondary: Small noise asymptotics

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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