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

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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.

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Authors and Affiliations

  1. Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN), ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    M. N. Gevorkyan, A. V. Demidova, T. R. Velieva, A. V. Korol’kova, D. S. Kulyabov & L. A. Sevast’yanov

  2. Laboratory of Information Technologies, Joint Institute for Nuclear Research, ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980, Russia

    D. S. Kulyabov

  3. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980, Russia

    L. A. Sevast’yanov

Authors
  1. M. N. Gevorkyan
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  2. A. V. Demidova
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  3. T. R. Velieva
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  4. A. V. Korol’kova
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  5. D. S. Kulyabov
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  6. L. A. Sevast’yanov
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Corresponding author

Correspondence to M. N. Gevorkyan.

Additional information

Original Russian Text © M.N. Gevorkyan, A.V. Demidova, T.R. Velieva, A.V. Korol’kova, D.S. Kulyabov, L.A. Sevast’yanov, 2018, published in Programmirovanie, 2018, Vol. 44, No. 2.

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Gevorkyan, M.N., Demidova, A.V., Velieva, T.R. et al. Implementing a Method for Stochastization of One-Step Processes in a Computer Algebra System. Program Comput Soft 44, 86–93 (2018). https://doi.org/10.1134/S0361768818020044

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  • DOI: https://doi.org/10.1134/S0361768818020044

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