Equivalence of measures for some class of Gaussian random fields

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Fractal Measures of the Sets Associated to Gaussian Random Fields

This paper summarizes recent results about the Hausdorff measure of the image, graph and level sets of Gaussian random fields, the packing dimension and packing measure of the image of fractional Brownian motion, the local times and multiple points of Gaussian random fields. Some open problems are also pointed out.

Extremes of a Class of Non-homogeneous Gaussian Random Fields

This contribution establishes exact tail asymptotics of sup(s,t)∈E X(s, t) for a large class of non-homogeneous Gaussian random fields X on a bounded convex set E ⊂ R, with variance function that attains its maximum on a segment on E. These findings extend the classical results for homogeneous Gaussian random fields and Gaussian random fields with unique maximum point of the variance. Applicati...

On the equivalence of Gaussian HMM and Gaussian HMM-like hidden conditional random fields

In this work we show that Gaussian HMMs (GHMMs) are equivalent to GHMM-like Hidden Conditional Random Fields (HCRFs). Hence, improvements of HCRFs over GHMMs found in literature are not due to a refined acoustic modeling but rather come from the more robust formulation of the underlying optimization problem or spurious local optima. Conventional GHMMs are usually estimated with a criterion on s...

Polarity of points for Gaussian random fields

We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic coefficients, such as the stochastic heat equation or wave equation with space-time white noise, or colored noise in spatial dimensions k ≥ 1. Our approach builds on...