  In this paper analogically as quadratic stochastic operators and processes we
define cubic stochastic operator (CSO) and cubic stochastic processes (CSP).
These are defined on the set of all probability measures of a measurable space.
The measurable space can be given on a finite or continual set. The finite case
has been investigated before. So here we mainly work on the continual set. We
give a construction of a CSO and show that dynamical systems generated by such
a CSO can be studied by studying of the behavior of trajectories of a CSO given
on a finite dimensional simplex. We define a CSP and drive differential
equations for such CSPs with continuous time.
