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

Ural Mathematical Journal

卷:4

Maxim A. Alshanskiy¹ 

[1] Ural Federal University, Ekaterinburg;

关键词: Brownian sheet, Cylindrical Wiener process, Gaussian white noise, Stochastic differential equation, Age-structured population model;   

DOI  :  10.15826/umj.2018.1.001

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown