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Proceedings of the Institute of Mathematics of the NAS of Belarus, 2025 Volume 33, Number 1, Pages 95–110 (Mi timb407)

COMPUTATIONAL MATHEMATICS

About one stochastic model of a dairy herd

A. Zhereloa, G. Krylova, V. Obolonkinb, M. Jorgensenc, R. Spelmand

a Belarusian State University, Minsk, Belarus
b Public Health Unit, Northland District Health Board, New Zealand
c University of Waikato, Hamilton, New Zealand
d Livestock Improvement Corporation, Hamilton, New Zealand

Abstract: The paper proposes a stochastic model, which describes the dynamics of biallelic polymorphism in a dairy herd. The proposed model assumes that the herd is formed under controlled mating conditions. The system of equations describing the model is based on the use of random processes containing jumps. A discrete analog of the stochastic system is constructed, for which a Monte Carlo simulation is performed.

Keywords: random process, stochastic differential equation, Ito integral, mathematical expectation, approximate calculations, Poisson process, Monte-Carlo method, gene dynamics.

UDC: 512.542

Received: 12.04.2025
Revised: 19.05.2025
Accepted: 23.05.2025



© Steklov Math. Inst. of RAS, 2025