The connection between the stochastic series and the time depending phenomena

Abstract

The present paper employs computer-assisted methods in order to solve different type of equations and systems.
The most significant goal is to transform, by modeling, time-depending series, such as stochastic series for
instance, into dynamic systems that can be solved, while also obtaining visual representations of their solutions.
So, we have started with an introduction including different computer-assisted methods for solving differential
equations and systems, followed by a proposed algorithm that leads to both an analytical formula and a graphical
representation of the optimal solution and command for a specific class of dynamical systems.
Through this work, we have shown that stochastic series can be expressed, through mathematical modeling, as a
time-dependent system of equations or even as dynamic system, which we have established an obvious similarity
with the generalised dynamic systems of the age-structured populations, discovered by J.R. Chasnov.
The connection which we have established allows for the application of the classical computer-assisted methods,
as well as particular algorithms, for many other time-dependent series, which can be modeled in the dynamic
system form, particularly when the main term follows a time-recurring formula.