Implementing a Method for Stochastization of One-Step Processes in a Computer Algebra System
Abstract
When modeling such phenomena as population dynamics, controllable ows, 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 rst principles by stochastization of one-step processes. Research can be represented as an iterative process that consists in obtaining a model and its further re nement. 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 di erential equations and their interaction schemes. The operation of the program is demonstrated on the Verhulst and Lotka-Volterra models.
Cite
@article{arxiv.1805.03190,
title = {Implementing a Method for Stochastization of One-Step Processes in a Computer Algebra System},
author = {D. S. Kulyabov and M. N. Gevorkyan and A. V. Demidova and T. R. Velieva and A. V. Korolkova and L. A. Sevastianov},
journal= {arXiv preprint arXiv:1805.03190},
year = {2018}
}
Comments
in English; in Russian