System response to partially known input

The available information on the random parameters in the definition of a variety of engineering, physics, biological, and other stochastic problems is usually insufficient for specifying the probability law of these parameters. Generally, there is a collection of probabilistic models consistent with the available information, referred to as the class of competing models. The paper examines the output of perfectly known deterministic systems subjected to partially specified input processes. It is shown that the class Cin of competing models for input can have many members and that the output properties may depend strongly on the particular member in Cin used to represent the input. Since the available information on the input is usually incomplete, it is rarely possible to find uniquely the output properties relevant for a stochastic problem. Simple linear and non-linear systems with quasi-static and dynamic output are used to illustrate the flow of information from input to output and assess the sensitivity of some output properties to the input model. The examples in the paper also show that estimates of a system performance can be inaccurate if based on input models selected by heuristic considerations.