Characterization and parameterization of a class of multivariable non-summable stochastic processes with bounded stochastic trends

Abstract

In some applications, multivariable stochastic processes that are composed of sequentially arranged independent weakly-stationary processes, may arise. Such multivariable process can be categorized as a class of non-summable processes with very complex probability density function. In this paper, we present the formal definition of such non-summable process, and provide a method of parameterizing and defining the statistical trend associated with the process. The illustration of a typical example of a multivariable non-summable process and how a bounded statistical trend can be obtained for the process is presented. The typical example is obtained from the simulation of a time-varying wideband wireless channel.