On stationary distributions of a stochastic difference equation with random coefficients

Recieved: 03/10/2025

Accepted: 04/07/2025

Keywords: stochastic difference equation, first-order autoregression with random coefficients, stationary distribution, mixture of normal laws

To cite this article

Korolev V.Yu., Romanyuk N.R. On stationary distributions of a stochastic difference equation with random coefficients. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2025. N 3, p.42-45 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–3–42–45.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Korolev V.Yu. (Lomonosov Moscow State University (MSU))
Romanyuk N.R. (Lomonosov Moscow State University (MSU))

Abstract

This paper shows that an arbitrary scale mixture of normal laws can be a stationary distribution of a stochastic difference equation (first-order autoregressive scheme) with random coefficients.

An example is given of what a (random) diffusion coefficient should look like for a particular mixture to be a stationary distribution.