Implementing a Method for Stochastization of One-Step Processes in a Computer Algebra System

Abstract

When modeling such phenomena as population dynamics, controllable flows, etc., a problem arises of adapting the existing models to a phenomenon under study. For this purpose, we propose to derive new models from the first principles by stochastization of one-step processes. Research can be represented as an iterative process that consists in obtaining a model and its further refinement. The number of such iterations can be extremely large. This work is aimed at software implementation (by means of computer algebra) of a method for stochastization of one-step processes. As a basis of the software implementation, we use the SymPy computer algebra system. Based on a developed algorithm, we derive stochastic differential equations and their interaction schemes. The operation of the program is demonstrated on the Verhulst and Lotka–Volterra models.