Some near-regular mechanical systems involve global deviations from their corresponding regular system. Despite extensive research on vibration analysis (eigensolution) of regular and local near-regular mechanical systems, the literature on vibration analysis of global near-regular mechanical systems is scant. In this paper, a method for vibration analysis of such systems was developed using Kr...

Large deviation principle for the non-linear functionals of non-Markovian models is a challenging subject. A class of such models are Gaussian processes. Among them, the fractional Brownian motions are perhaps the most important processes. In this talk, I will talk about some recent progress achieved in the large deviations for local times and intersection local times of fractional Brownian mot...

We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times

We study large deviations for intersection local times of p independent d-dimensional symmetric stable processes of index β, under the condition p(d − β) < d. Our approach is based on FeynmanKac type large deviations, moment computations and some techniques from probability in Banach spaces.

Radial frequency (RF) patterns have been used to study the processes involved in shape perception. The psychophysical literature suggests that there are distinct global and local shape detection processes for low and high radial frequency patterns, but this has not been tested in a combined contour pattern, such as would be needed to describe the contours of most natural objects. Here, we combi...

Goodness-of-fit evaluation of a parametric regression model is often done through hypothesis testing, where the fit of the model of interest is compared statistically to that obtained under a broader class of models. Nonparametric regression models are frequently used as the latter type of model, because of their flexibility and wide applicability. To date, this type of tests has generally been...