Large deviations for processes with discontinuous statistics
This paper is devoted to the problem of sample path large deviations for the Markov processes on \({\mathbb R}^N\) having a constant but different transition mechanism on each boundary set \(B_\Lambda=\{x:~x_j=0\) for \(i\not \in \Lambda\), \(x_j>0\) for \(j\in \Lambda\},\) where \(\Lambda\) is a subset of \(\{1,\dots,N\}\). The global sample path large deviation principle and an integral representation of the rate function are derived from local large deviation estimations. These results complete the proof of Dupuis and Ellis of the sample path large deviation principle for Markov processes describing a general class of queueing networks.
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