scholarly journals On local times of anisotropic Gaussian random fields

2011 ◽  
Vol 5 (1) ◽  
Author(s):  
Dongsheng Wu ◽  
Yimin Xiao
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
Local Times

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

scholarly journals Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections

2008 ◽  
Vol 40 (02) ◽  
pp. 529-547
Author(s):  
Francisco J. Piera ◽  
Ravi R. Mazumdar ◽  
Fabrice M. Guillemin
Keyword(s):  
Random Fields ◽  
Diffusion Coefficients ◽  
Boundary Behavior ◽  
Stationary Regime ◽  
Product Form ◽  
Local Times ◽  
Nonnegative Orthant ◽  
State Dependent ◽  
The Times ◽  
And Diffusion

In this paper we consider reflected diffusions with positive and negative jumps, constrained to lie in the nonnegative orthant of ℝ n . We allow for the drift and diffusion coefficients, as well as for the directions of reflection, to be random fields over time and space. We provide a boundary behavior characterization, generalizing known results in the nonrandom coefficients and constant directions of the reflection case. In particular, the regulator processes are related to semimartingale local times at the boundaries, and they are shown not to charge the times the process expends at the intersection of boundary faces. Using the boundary results, we extend the conditions for product-form distributions in the stationary regime to the case when the drift and diffusion coefficients, as well as the directions of reflection, are random fields over space.

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