We study the large deviations principle for locally periodic SDEs with small noise and fast oscillating coefficients. There are three regimes depending on how fast the intensity of the noise goes to zero relative to homogenization parameter. We use weak convergence methods which provide...

Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set B before another set A, and it is assumed that this probability satisfies a large deviation scaling. A notion of subsolution is defined for the...

This paper considers the problem of rate function identification for multidimensional queueing models with feedback. A set of techniques are introduced which allow this identification when the model possesses certain structural properties. The main tools used are representation formulas for...

We consider the exponential decay rate of the stationary tail probabilities of reflected Brownian motion X in the N-dimensional orthant having drift b, covariance matrix A, and constraint matrix D. Suppose that the Skorokhod or reflection mapping associated with the matrix D is well-defined and...

We investigate, by means of an example, the large deviations principle for the empirical measure of a Markov chain when Feller continuity properties are not assumed. Using the weak convergence approach, we explicitly compute the resulting rate function, and find that it is not of the...

Stochastic partial differential equations driven by Poisson random measures (PRMs) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential equation (PDE). A systematic framework for the study of...