Gibbs derivatives in linear system theory

Abstract

In this paper we first give a general characterization of Gibbs derivatives on groups and then discuss their use in linear systems theory considering systems with both deterministic and stochastic input/output signals. We introduce the concept of p-adic linear stochastic systems, offering in that way another field for the application of Gibbs derivatives in a manner corresponding to that used in the theory of dyadic systems and stochastic dyadic systems.