2017-12 06/11/2017 ForsChem Research Reports 2017-12 (1 / 19) www.forschem.org Ergodic-Stochastic Transformations Hugo Hernandez ForsChem Research, 050030 Medellin, Colombia hugo.hernandez@forschem.org doi: 10.13140/RG.2.2.20325.70881 Abstract Deterministic dynamic variables can be transformed into random stochastic variables by means of an ergodic-stochastic transformation. Such transformation is inspired on the ergodic hypothesis, which relates the probability of a system taking a certain state value with the time spent by the system at such state. In the current report, the mathematical derivation of such ergodic-stochastic transformation is presented. Additionally, a numerical alternative is provided for those systems that cannot be solved analytically. Through different application examples, the ergodic-stochastic transformation is explained and illustrated. Keywords Dynamic processes, Ergodic hypothesis, Random variables, Stochastic modeling, Transformations. 1. Introduction Randomness, the apparent lack of predictability of occurrence of future events, is actually the result of our lack of knowledge about the factors and mechanisms influencing those future events. Even purely deterministic processes can be transformed into stochastic processes just by assuming that information about a single variable is missing. Let us for example consider an analog wall clock operating flawlessly. If at any given moment a person see the position of the clock’s second hand, it will be possible for such person to predict the position of the second hand in the future. If the same person did not have the chance to see the clock previously, and is then asked about the position of the second hand in exactly 60 seconds, the answer given will be random, as it will be only a guess based on the limited information available.