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 | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.