Upper bounds on the response variance of stochastic systems via generalized variability response functions

摘要

This paper describes several attributes of the classical variability response function (VRF) whose main use is to establish upper bounds on the response variability of stochastic systems whose properties are described by random fields. Certain limitations of the classical VRF are discussed. The generalized variability response function (GVRF) is then introduced with the aid of the concept of associated fields, as a means of overcoming the limitations of the classical VRF. It is conjectured that the GVRF can be used to establish spectral- and probability-distribution-free upper bounds on the response variability with a wide range of applicability.