A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES

A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES

Under consideration is construction of a model of age-structured population reflecting random oscillations of the death and birth rate functions. We arrive at an Itô-type difference equation in a Hilbert space of functions which can not be transformed into a proper Itô equation via passing to the li...

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Main Author: Maxim A. Alshanskiy
Format: Article
Language:English
Published: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. 2018-07-01
Series:Ural Mathematical Journal
Subjects:
Brownian sheet, Cylindrical Wiener process, Gaussian white noise, Stochastic differential equation, Age-structured population model
Online Access:https://umjuran.ru/index.php/umj/article/view/106
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spelling doaj-41219fc373394801bc61c7f50314773d2020-11-24T21:58:29ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. Ural Mathematical Journal2414-39522018-07-014110.15826/umj.2018.1.00153A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATESMaxim A. Alshanskiy0Ural Federal University, EkaterinburgUnder consideration is construction of a model of age-structured population reflecting random oscillations of the death and birth rate functions. We arrive at an Itô-type difference equation in a Hilbert space of functions which can not be transformed into a proper Itô equation via passing to the limit procedure due to the properties of the operator coefficients. We suggest overcoming the obstacle by building the model in a space of Hilbert space valued generalized random variables where it has the form of an operator-differential equation with multiplicative noise. The result on existence and uniqueness of the solution to the obtained equation is stated.https://umjuran.ru/index.php/umj/article/view/106Brownian sheet, Cylindrical Wiener process, Gaussian white noise, Stochastic differential equation, Age-structured population model
collection DOAJ
language English
format Article
sources DOAJ
author Maxim A. Alshanskiy
spellingShingle Maxim A. Alshanskiy
A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES
Ural Mathematical Journal
Brownian sheet, Cylindrical Wiener process, Gaussian white noise, Stochastic differential equation, Age-structured population model
author_facet Maxim A. Alshanskiy
author_sort Maxim A. Alshanskiy
title A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES
title_short A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES
title_full A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES
title_fullStr A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES
title_full_unstemmed A MODEL OF AGE–STRUCTURED POPULATION UNDER STOCHASTIC PERTURBATION OF DEATH AND BIRTH RATES
title_sort model of age–structured population under stochastic perturbation of death and birth rates
publisher Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
series Ural Mathematical Journal
issn 2414-3952
publishDate 2018-07-01
description Under consideration is construction of a model of age-structured population reflecting random oscillations of the death and birth rate functions. We arrive at an Itô-type difference equation in a Hilbert space of functions which can not be transformed into a proper Itô equation via passing to the limit procedure due to the properties of the operator coefficients. We suggest overcoming the obstacle by building the model in a space of Hilbert space valued generalized random variables where it has the form of an operator-differential equation with multiplicative noise. The result on existence and uniqueness of the solution to the obtained equation is stated.
topic Brownian sheet, Cylindrical Wiener process, Gaussian white noise, Stochastic differential equation, Age-structured population model
url https://umjuran.ru/index.php/umj/article/view/106
work_keys_str_mv AT maximaalshanskiy amodelofagestructuredpopulationunderstochasticperturbationofdeathandbirthrates
AT maximaalshanskiy modelofagestructuredpopulationunderstochasticperturbationofdeathandbirthrates
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