Electronic Journal of Probability
- Electron. J. Probab.
- Volume 8 (2003), paper no. 16, 46 p.
Large Deviations for the Emprirical Measures of Reflecting Brownian Motion and Related Constrained Processes in $R_+$
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.
Electron. J. Probab., Volume 8 (2003), paper no. 16, 46 p.
First available in Project Euclid: 23 May 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F10: Large deviations
Secondary: 60J25: Continuous-time Markov processes on general state spaces 93E20: Optimal stochastic control
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