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


Дәйексөз келтіру

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Аннотация

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.

Авторлар туралы

M. Gevorkyan

Department of Applied Probability and Informatics

Хат алмасуға жауапты Автор.
Email: gevorkyan_mn@rudn.university
Ресей, ul. Miklukho-Maklaya 6, Moscow, 117198

A. Demidova

Department of Applied Probability and Informatics

Email: gevorkyan_mn@rudn.university
Ресей, ul. Miklukho-Maklaya 6, Moscow, 117198

T. Velieva

Department of Applied Probability and Informatics

Email: gevorkyan_mn@rudn.university
Ресей, ul. Miklukho-Maklaya 6, Moscow, 117198

A. Korol’kova

Department of Applied Probability and Informatics

Email: gevorkyan_mn@rudn.university
Ресей, ul. Miklukho-Maklaya 6, Moscow, 117198

D. Kulyabov

Department of Applied Probability and Informatics; Laboratory of Information Technologies

Email: gevorkyan_mn@rudn.university
Ресей, ul. Miklukho-Maklaya 6, Moscow, 117198; ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980

L. Sevast’yanov

Department of Applied Probability and Informatics; Bogoliubov Laboratory of Theoretical Physics

Email: gevorkyan_mn@rudn.university
Ресей, ul. Miklukho-Maklaya 6, Moscow, 117198; ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980

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