Romanyuk N.R.

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.

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.