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The Annals of Applied Probability 1998, Vol. 8, No. 1, 4566
 

Summary: The Annals of Applied Probability
1998, Vol. 8, No. 1, 45­66
ON LARGE DEVIATIONS OF MARKOV PROCESSES
WITH DISCONTINUOUS STATISTICS1
By Murat Alanyali2
and Bruce Hajek
Bell Laboratories and University of Illinois, Urbana­Champaign
This paper establishes a process-level large deviations principle for
Markov processes in the Euclidean space with a discontinuity in the tran-
sition mechanism along a hyperplane. The transition mechanism of the
process is assumed to be continuous on one closed half-space and also
continuous on the complementary open half-space. Similar results were
recently obtained for discrete time processes by Dupuis and Ellis and by
Nagot. Our proof relies on the work of Blinovskii and Dobrushin, which in
turn is based on an earlier work of Dupuis and Ellis.
1. Overview of previous work. Large deviations of Markov processes
with discontinuous transition mechanisms arise in a broad range of applica-
tions such as the analysis of load sharing and queueing networks [see Alanyali
and Hajek (1998) and Dupuis and Ellis (1995) for examples]. This paper es-
tablishes a large deviations principle (LDP) for a Markov random process

  

Source: Alanyali, Murat - Department of Electrical and Computer Engineering, Boston University

 

Collections: Engineering