Stochastic oscillations of a dynamical system in the case of a normal and Poisson distribution of a random coefficient

Abstract

Background. Equations with random coefficients serve as a mathematical model for a number of problems that arise in practice. The solution, in this case, will be a stochastic process. Its dependence on nondeterministic parameters is interesting. This relationship can be established by calculating some statistical characteristics of the solution, such as the mathematical expectation. Materials and methods. We consider the initial problem for a second-order inhomogeneous differential equation with random parameters and pose the problem of finding the mathematical expectation of its solution. Results. Analytical formulas for the mathematical expectation of the solution of a stochastic differential equation in the case of the normal and Poisson distribution laws of a random coefficient are obtained. Conclusions. The obtained formulas allow us to study the dependence of the solution of a stochastic problem on nondeterministic parameters.

Keywords

• mathematical expectation
• equation with random coefficients
• normal distribution
• poisson distribution