Sojourn functionals for spatiotemporal Gaussian random fields with long memory

Skew-Gaussian Random Fields

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...

Gaussian Process Random Fields

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via pairwise potentials. The GPRF likelihood is a simple, tractable, and paralle...

Credit Risk Modeling with Gaussian Random Fields

The literature on credit risk consists of different approaches in modeling the behavior of defaultable bonds. The structural approach is based on the evolution of the firm value to determine default and recovery. In contrast, the more recently developed intensity-based models specify the default time exogenously. In this approach the defaultable yield curve results from the risk-free yield curv...

Central Limit Theorems for Non-Linear Functionals of Gaussian Fields

In the present paper it is shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero. The results are formulated in terms of the Hermite rank of the functional and of the rate of the correlation function. Then we show an example when the limit field is self-similar and Ga...

Local Functionals and Generalized Random Fields