State space calculations for discrete probability densities
State space methods have proved to be powerful theoretical and computational tools in a number of areas of applications. In this paper, state space methods are applied for the study of discrete probability densities on the set \([0,1,2,\dots]\). The fundamental approach is to consider the class of all discrete probability densities that can be represented as the impulse response-convolution kernel of a finite-dimensional discrete time, state space system. It is shown that all standard operations, such as the calculation of moments, convolution, scaling, translation, product, etc., can be carried out making use of the system representations.
scientific article; zbMATH DE number 1790258