Regression approximations of wavelength and amplitude distributions

Abstract

A regression approximation of wavelength and amplitude distribution in an almost surely continuous process η ( t ), is based on a successively more detailed decomposition, η ( t ) = η n ( t ) + Δ n ( t ), into one regression term η n on n suitably chosen random quantities, and one residual process Δ n . The distances between crossings, maxima, etc., are then approximated by the corresponding quantities in the regression term, and explicit expressions given for the densities of these quantities.