EXPECTED NUMBER OF CROSSINGS OF AN ARBITRARY CURVE BY A NON-STATIONARY GAUSSIAN PROCESS by

On Crossings of Arbitrary Curves by Certain Gaussian Processes1

under conditions which are very close to the necessary ones. Here N(T) is the number of crossings of the level u in (0, T) by the stationary Gaussian process x(t), with covariance function r(r). The symbol £ denotes expectation. The treatment of this problem given by Bulinskaya is essentially a rigorization of the method used by Grenander and Rosenblatt [4], which in turn extends an argument du...

On the average number of sharp crossings of certain Gaussian random polynomials

On the Second Moment of the Number of Crossings by a Stationary Gaussian Process

to have a finite variance of the number of zeros of a centered stationary Gaussian process with twice differentiable covariance function r. This condition is known as the Geman condition, since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows that the Geman condition is sti...

Level crossings and other level functionals of stationary Gaussian processes

Abstract: This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal comparison method, Rice method, Stein...

Robust Distributed Source Coding with Arbitrary Number of Encoders and Practical Code Design Technique

The robustness property can be added to DSC system at the expense of reducing performance, i.e., increasing the sum-rate. The aim of designing robust DSC schemes is to trade off between system robustness and compression efficiency. In this paper, after deriving an inner bound on the rate–distortion region for the quadratic Gaussian MDC based RDSC system with two encoders, the structure of...