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

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. © 2018, Pleiades Publishing, Ltd.

Редакторы
-
Издательство
-
Номер выпуска
2
Язык
Английский
Страницы
86-93
Статус
Опубликовано
Подразделение
-
Номер
-
Том
44
Год
2018
Организации
  • 1 Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN), ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
  • 2 Laboratory of Information Technologies, Joint Institute for Nuclear Research, ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980, Russian Federation
  • 3 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, ul. Zholio-Kyuri 6, Dubna, Moscow oblast 141980, Russian Federation
Ключевые слова
Differential equations; Iterative methods; Stochastic systems; Computer algebra; Computer algebra systems; Controllable flow; First principles; Interaction schemes; Iterative process; Software implementation; Stochastic differential equations; Algebra
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6804/