A Berry-Esseen Bound for Nonlinear Statistics with Bounded Differences

In this paper, we obtain an explicit Berry-Esseen bound in the central limit theorem for nonlinear statistics with bounded differences. Some examples are provided as well.

Linear and nonlinear statistics of extreme waves

The probability of extremely high waves is calculated by two methods. The first method is based on the direct numerical simulation of two-dimensional wave field using a three-dimensional nonlinear model. The second method consists in calculation of the probability of wave heights over ensemble of fields representing a superposition of linear waves with random phases and a spectrum similar to that obtained in the nonlinear model. It is shown that the integral probability of extreme waves are very close to each other in both cases. This implies that the role of nonlinearity in the generation of extreme waves is probably not so important as it was assumed in most papers considering this phenomenon.