How far can stochastic and deterministic views be reconciled?

TL;DR

This paper explores the similarities and differences between stochastic and deterministic processes, highlighting that their practical behaviors may be more closely aligned than traditionally assumed.

Contribution

It provides a pedagogical overview of stochastic and deterministic processes and demonstrates that their behavioral gap can be surprisingly small in practice.

Findings

Stochastic and deterministic processes share more similarities than expected.

The behavioral differences between the two can be minimal in practical scenarios.

A basic mathematical framework for stochastic processes is presented.

Abstract

In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical description of stochastic processes is also given. Our main aim is to illustrate the somehow surprising fact that the gap between the behaviour of stochastic and deterministic processes might, from a practical perspective, be much smaller than a priori expected.