Electronic Journal of Probability

Large Deviations for the Emprirical Measures of Reflecting Brownian Motion and Related Constrained Processes in $R_+$

Amarjit Budhiraja and Paul Dupuis

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Abstract

We consider the large deviations properties of the empirical measure for one dimensional constrained processes, such as reflecting Brownian motion, the M/M/1 queue, and discrete time analogues. Because these processes do not satisfy the strong stability assumptions that are usually assumed when studying the empirical measure, there is significant probability (from the perspective of large deviations) that the empirical measure charges the point at infinity. We prove the large deviation principle and identify the rate function for the empirical measure for these processes. No assumption of any kind is made with regard to the stability of the underlying process.

Article information

Source
Electron. J. Probab., Volume 8 (2003), paper no. 16, 46 p.

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464037589

Digital Object Identifier
doi:10.1214/EJP.v8-154

Mathematical Reviews number (MathSciNet)
MR1998761

Zentralblatt MATH identifier
1064.60044

Subjects
Primary: 60F10: Large deviations
Secondary: 60J25: Continuous-time Markov processes on general state spaces 93E20: Optimal stochastic control

Keywords
Markov process constrained process large deviations empirical measure stability reflecting Brownian motion

Citation

Budhiraja, Amarjit; Dupuis, Paul. Large Deviations for the Emprirical Measures of Reflecting Brownian Motion and Related Constrained Processes in $R_+$. Electron. J. Probab. 8 (2003), paper no. 16, 46 p. doi:10.1214/EJP.v8-154. https://projecteuclid.org/euclid.ejp/1464037589


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