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Large deviations bounds for face-homogeneous random walks in the quarter-plane. (English) Zbl 1336.60092
Summary: In this article, we analyze the large deviations bounds for the nonergodic face-homogeneous random walk in the positive quadrant. Under some condition the value of the local rate function for the path identically equal to zero is found, and an explicit expression is derived for it. This makes the computation of its value possible for specific stochastic networks. Some numerical examples are given.

60G50 Sums of independent random variables; random walks
60F10 Large deviations
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