General Marshall-Olkin Models, Dependence Orders and Comparisons of Environmental Processes

In many applicative fields, the behavior of a process Z is assumed to be subjected to an underlying process X that describes evolutions of environmental conditions. A common way to define the environmental process is by letting the marginal values of X subjected to specific environmental factors (constant along time) and factors describing the conditions of the environment at the specified time. In this paper we describe some recent results that can be used to compare two of such environmental discrete-time processes X1 and X2 in dependence. A sample of applications of the effects of these comparison results on the corresponding processes Z1 and Z2 in some different applicative contexts are provided.