Abstract:
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.
Keywords:Brownian sheet, Cylindrical Wiener process, Gaussian white noise, Stochastic differential equation, Age-structured population model.
This work was supported by the Program for State Support of Leading Scientific Schools of the Russian Federation (project no. NSh-9356.2 016.1) and by the Competitiveness Enhancement Program of the Ural Federal University (Enactment of the Government of the Russian Federation of March 16, 2013 no. 211, agreement no. 02 .A03.21.0 006 of August 27, 2013).
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Maxim A. Alshanskiy, “A model of age-structured population under stochastic perturbation of death and birth rates”, Ural Math. J., 4:1 (2018), 3–13
\Bibitem{Als18}
\by Maxim~A.~Alshanskiy
\paper A model of age-structured population under stochastic perturbation of death and birth rates
\jour Ural Math. J.
\yr 2018
\vol 4
\issue 1
\pages 3--13
\mathnet{http://mi.mathnet.ru/umj51}
\crossref{https://doi.org/10.15826/umj.2018.1.001}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR3848660}
\elib{https://elibrary.ru/item.asp?id=35339278}
Linking options:
https://www.mathnet.ru/eng/umj51
https://www.mathnet.ru/eng/umj/v4/i1/p3
This publication is cited in the following 1 articles:
Arcady Ponosov, Lev Idels, Ramazan Kadiev, “Stochastic McKendrick–Von Foerster models with applications”, Physica A: Statistical Mechanics and its Applications, 537 (2020), 122641