Sample Path Large Deviations for Laplacian Models in (1 + 1)-dimensions

Warwick.ac.uk/lib-publications Sample Path Large Deviations for Laplacian Models in (1 + 1)-dimensions

We study scaling limits of a Laplacian pinning model in (1 + 1) dimension and derive sample path large deviations for the profile height function. The model is given by a Gaussian integrated random walk (or a Gaussian integrated random walk bridge) perturbed by an attractive force towards the zero-level. We study in detail the behaviour of the rate function and show that it can admit up to five...

Sample Path Large Deviations for Queueing Networks with Bernoulli Routing

This paper is devoted to the problem of sample path large deviations for multidimensional queueing models with feedback. We derive a new version of the contraction principle where the continuous map is not well-defined on the whole space: we give conditions under which it allows to identify the rate function. We illustrate our technique by deriving a large deviation principle for a class of net...

SAMPLE PATH LARGE DEVIATIONS FOR QUEUES WITH MANY INPUTS 1 By Damon

Large Deviations with Diminishing Rates

The theory of large deviations for jump Markov processes has been generally proved only when jump rates are bounded below, away from zero (Dupuis and Ellis, 1995, The large deviations principle for a general class of queueing systems I. Trans. Amer. Math. Soc. 347 2689–2751; Ignatiouk-Robert, 2002, Sample path large deviations and convergence parameters. Ann. Appl. Probab. 11 1292–1329; Shwartz...

Large Deviations with Diminishing Rate

The theory of large deviations for jump Markov processes has been generally proved only when jump rates are bounded below, away from zero [4, 8, 12]. Yet various applications of interest do not satisfy this condition. We describe several classes of models where jump rates diminish to zero in a Lipschitz continuous way. Under appropriate conditions, we prove that the sample path large deviations...