Stationary Gaussian Field Research Articles

A simulation method for stationary Gaussian random functions based on the sampling theorem

A unified method is developed for simulating realizations of real-valued stationary Gaussian processes, vector processes, fields, and vector fields. The method is based on parametric random models consisting of superpositions of deterministic functions of time or space with random amplitudes. The parametric models are based on the sampling theorem for random processes and generalizations of it for vector processes and random fields. The proposed simulation method is efficient and uses algorithms for generating realizations of random processes and fields that are similar to simulation techniques based on ARMA models. Several examples are presented to demonstrate the proposed simulation method and evaluate its efficiency and accuracy.

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 Gaussian but not necessarily consisting of independent elements.

Photon Counting Statistics of a Stationary Gaussian Field with Brillouin Spectrum

The statistical characteristics of a stationary gaussian field endowed with Brillouin spectrum are studied. A closed-form expression for the exact one-fold generating function (g.f.) corresponding to the arbitrary count rates and the sample times is derived. The time-interval distribution of the photon counting statistics is extracted from the g.f. without resort to any approximate procedures. Comparison with the earlier results obtained by use of the approximate methods shows that the error in such approximations is considerable.

Wave induced vibrations of gravity platforms: a stochastic theory

This paper presents a consistent stochastic method to evaluate wave induced vibrations of offshore platforms with special emphasis on gravity type structures. The wavy sea surface is idealized as a stationary and homogeneous stochastic Gaussian (or semi-Gaussian) field. The wave loading processes are treated by applying the concepts of probabilistic potential theory and the stochastic linearization method. The structure is modelled according to the finite element method using boundary spring-dashpot elements to idealize the soil-foundation system. The linearized equations of motion are solved by the frequency response method accounting properly for the temporal and spatial structure of waves as well as for time dependent system function. Numerical results for a 170m high concrete platform are presented including a parametric study of effects due to the shape of the wave spectral density.

The mean number of maxima above high levels in Gaussian random fields

An asymptotic formula for the mean number of maxima above a level of an n-dimensional stationary Gaussian field has been given by Nosko without proof. In this note a short general proof of this formula is given.

The mean number of maxima above high levels in Gaussian random fields

An asymptotic formula for the mean number of maxima above a level of an n-dimensional stationary Gaussian field has been given by Nosko without proof. In this note a short general proof of this formula is given.

Statistical Properties of Optical Fields Scattered by Random Media Application to Rotating Ground Glass

We give a sufficient condition for the field scattered from a surface (S) illuminated by a laser beam to be a stationary gaussian field. This condition is fulfilled for the optical shot noise. As an example we calculate the spectrum of the field scattered from a granular surface. We show that it does not depend on the statistical properties of (S) when the number of grains tends to infinity.

Generalizations of Gaussian Optical Fields

Stationary Gaussian optical fields are also often called thermal fields because they are generated by natural or thermal sources. By using the amplitude of the field, we show that thermal fields are only a particular case of the more general class of Gaussian fields. Such nonthermal Gaussian fields can be obtained experimentally, and we calculate some properties, concerning particularly the effect of Hanbury Brown and Twiss, photocounting, and coincidence experiments. We show that the thermal fields are the less chaotic or incoherent Gaussian fields. Finally, we introduce pseudo-Gaussian fields which appear in some experiments of diffusion with laser light. They are non-Gaussian fields, but their intensity has the same properties as that of a Gaussian field.