Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications

In this paper, we study the limit distributions of upper and lower record values of a stationary Gaussian sequence under an equi-correlated set up. Moreover, the class of limit distribution functions (df’s) of the joint upper (and the lower) record values of a stationary Gaussian sequence is fully characterized. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.

Nonlinear System Identification with a Real–Coded Genetic Algorithm (RCGA)

This paper is devoted to the blind identification problem of a special class of nonlinear systems, namely, Volterra models, using a real-coded genetic algorithm (RCGA). The model input is assumed to be a stationary Gaussian sequence or an independent identically distributed (i.i.d.) process. The order of the Volterra series is assumed to be known. The fitness function is defined as the difference between the calculated cumulant values and analytical equations in which the kernels and the input variances are considered. Simulation results and a comparative study for the proposed method and some existing techniques are given. They clearly show that the RCGA identification method performs better in terms of precision, time of convergence and simplicity of programming.

Asymptotic Expansion for the Distribution and Density Functions of the Quadratic Form of a Stationary Gaussian Process in the Large Deviation Cramer Zone

The work considers the asymptomic expansions in the large deviation Cramer zone for the distribution and its density functions of the quadratic form a stationary Gaussian sequence. To this end the general authors lemma [1], [3] for an arbitrary random variable with regular behavior of its cumulants is used.