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Applied Mathematics & Optimization, 1980
Nonanticipative representations of Gaussian random fields equivalent to the two-parameter Wiener process are defined, and necessary and sufficient conditions for their existence derived. When such representations exist they provide examples of canonical representations of multiplicity one. In contrast to the one-parameter case, examples are given where
Bromley, C., Kallianpur, Gopinath
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Nonanticipative representations of Gaussian random fields equivalent to the two-parameter Wiener process are defined, and necessary and sufficient conditions for their existence derived. When such representations exist they provide examples of canonical representations of multiplicity one. In contrast to the one-parameter case, examples are given where
Bromley, C., Kallianpur, Gopinath
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Structures in random fields: Gaussian fields
Physical Review A, 1992We present two alternative methods for evaluating the probability densities of structures defined by d degrees of freedom in random fields. For Gaussian random fields, both differentiable and nondifferentiable, the application of these methods is considered in detail.
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Foundations of Physics, 1978
Two results on Gaussian random fields are presented. The first characterizes the unit Gaussian random field by a strong independence property and the second determines Gaussian random fields that are generated by stochastic processes.
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Two results on Gaussian random fields are presented. The first characterizes the unit Gaussian random field by a strong independence property and the second determines Gaussian random fields that are generated by stochastic processes.
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Applied and Computational Harmonic AnalysisWe derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method.
Adil Salim +2 more
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2020
Gaussian random fields have a long history in science that dates back to the research of Andrey Kolmogorov and his group. Their investigation remains an active field of research with many applications in physics and engineering. The widespread appeal of Gaussian random fields is due to convenient mathematical simplifications that they enable, such as ...
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Gaussian random fields have a long history in science that dates back to the research of Andrey Kolmogorov and his group. Their investigation remains an active field of research with many applications in physics and engineering. The widespread appeal of Gaussian random fields is due to convenient mathematical simplifications that they enable, such as ...
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Local Additive Functionals of Gaussian Random Fields
Theory of Probability & Its Applications, 1984Translation from Teor. Veroyatn. Primen. 28, No.1, 32-44 (Russian) (1983; Zbl 0521.60059).
Dobrushin, R. L., Kel'bert, M. Ya.
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Latin Hypercube Sampling of Gaussian Random Fields
Technometrics, 1999Following the method of Stein, this article shows how a Latin hypercube sample can be drawn from a Gaussian random field. In a case study the efficiency of Latin hypercube sampling is compared experimentally to that of simple random sampling. The model outputs studied are the mean and the 5- and 95-percentile of the areal fraction where point ...
Pebesma, E.J., Heuvelink, G.B.M.
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1998
Recall, a family {ξ} of real valued random variables is called Gaussian if the joint probability distribution of these (taken in finite number) random variables is Gaussian. The Gaussian probability distribution in R n of random variables (ξ 1,..., ξ n ) has the characteristic function $$ Eexp\left\{ {i\sum\limits_{k = 1}^n {{\lambda _k}{\zeta _k}}
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Recall, a family {ξ} of real valued random variables is called Gaussian if the joint probability distribution of these (taken in finite number) random variables is Gaussian. The Gaussian probability distribution in R n of random variables (ξ 1,..., ξ n ) has the characteristic function $$ Eexp\left\{ {i\sum\limits_{k = 1}^n {{\lambda _k}{\zeta _k}}
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Neural Gaussian Conditional Random Fields
2014We propose a Conditional Random Field (CRF) model for structured regression. By constraining the feature functions as quadratic functions of outputs, the model can be conveniently represented in a Gaussian canonical form. We improved the representational power of the resulting Gaussian CRF (GCRF) model by (1) introducing an adaptive feature function ...
Vladan Radosavljevic +2 more
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1994
After some general results relating mixing properties of a Gaussian random field, we propose an explicit bound of the mixing coefficients of such a random field based on the approximation properties of its spectral density in § 2.1.1. In § 2.1.2. more precise results characterize the decay of such coefficients for Gaussian processes. In this chapter, X
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After some general results relating mixing properties of a Gaussian random field, we propose an explicit bound of the mixing coefficients of such a random field based on the approximation properties of its spectral density in § 2.1.1. In § 2.1.2. more precise results characterize the decay of such coefficients for Gaussian processes. In this chapter, X
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