title: ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð° Ð¼Ð¾Ð¼ÐµÐ½ÑÐ¾Ð² Ð´Ð»Ñ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ð³Ð¾ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ñ Ð¸Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐµÐ°ÐºÑÐ¸Ð¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Applying method of moments to approximate some solutions of chemical master equation
Creators: name: ÐÐ°ÑÑÑÐ½Ð¾Ð²Ð°, ÐÐºÐ°ÑÐµÑÐ¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ðµ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ
Ð¼ÐµÑÐ¾Ð´ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ¾Ð²
Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ðµ-Ð³Ð¸Ð±ÐµÐ»Ñ
ÑÑÐ¾Ñ Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¿ÑÐ¾ÑÐµÑÑÑ
Ð¼Ð¾Ð½Ð¾Ð¼Ð¾Ð»ÐµÐºÑÐ»ÑÑÐ½ÑÐµ ÑÐµÐ°ÐºÑÐ¸Ð¸
chemical master equation
method of moments
birth-death model
stochastic processes
unimolecular reactions

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description: The study considers the approximation of the chemical master equation by the method of moments, also considers the problem of restoring the distribution of its moments. The relevance of the study is considered in the context of gene expression. The tasks that were solved during the study: to study the derivation of the chemical master equation, to consider approaches to its solution, to derive a system of moment equations for a monomolecular birth-to-death reaction, to solve the problem of reconstructing the probability distribution over moments for the birth-death model. Compare the exact solution and the resulting approximation. In the course of work in the programming language R, with the help of the optimx package, the optimization problem was solved for reconstructing the probability distribution by the Bruyden â Fletcher â Goldfarb â Shanno method. As a result, some methods for solving the chemical master equation on were considered, an exact solution of the chemical master equation for the birth-death model was obtained, and the reconstruction of the probability distribution for a given monomolecular reaction from the moments using the maximum entropy method was analyzed.