On the stationary distribution of a multivariate stochastic difference equation with random coefficients

Recieved: 07/15/2025

Accepted: 02/20/2026

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

Available in the on-line version with: 24.07.2026

To cite this article

Korolev V.Yu., Romanyuk N.R. On the stationary distribution of a multivariate stochastic difference equation with random coefficients. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2026. N 2, p.43-39 https://doi.org/10.55959/MSU/0137–0782–15–2026–50–2–43–49.

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

It is shown that any scaled mixture of multivariate normal distributions can be a stationary distribution in the multivariate stochastic difference equation (SDE) scheme—a first-order multivariate autoregression with random coefficients. A correspondence is established between the resulting mixture and the behavior of the coefficients generating the stationary distribution.