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 Electronic Journal of Probability > Vol. 8 (2003) > Paper 16 open journal systems 


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

Amarjit Budhiraja, University of North Carolina at Chapel Hill
Paul Dupuis, Brown University


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.


Full text: PDF

Pages: 1-46

Published on: September 15, 2003
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Electronic Journal of Probability. ISSN: 1083-6489