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

Maxim A. Alshanskiy     (Ural Federal University, Ekaterinburg, Russian Federation)

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

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References


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DOI: http://dx.doi.org/10.15826/umj.2018.1.001

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