A model of age-structured population under stochastic perturbation of death and birth rates. (English) Zbl 1453.60112

Alshanskiy, Maxim A.

Ural Math. J. 4, No. 1, 3-13 (2018).

Summary: 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.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60H40	White noise theory
92D25	Population dynamics (general)

Keywords:

Brownian sheet; cylindrical Wiener process; Gaussian white noise; stochastic differential equation; age-structured population model

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