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Abstract <p>It is shown that an arbitrary normal variance-mean mixture can be a stationary distribution of a stochastic difference equation or first order autoregressive process with random coefficients. An example is presented of what the (random) drift and diffusion coefficients must look like to provide that a certain variance-mean mixture is a stationary distribution of such a process. It is also shown that a stationary mode of the first-order autoregressive process possesses the stability property.</p>

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Normal Variance-Mean Mixtures as Stationary Distributions of Stochastic Difference Equations with Random Coefficients

  • 期刊论文

  • 发表日期：

    2026年7月26日

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  • V. Yu. Korolev,
  • N. R. Romanyuk

摘要

Abstract

It is shown that an arbitrary normal variance-mean mixture can be a stationary distribution of a stochastic difference equation or first order autoregressive process with random coefficients. An example is presented of what the (random) drift and diffusion coefficients must look like to provide that a certain variance-mean mixture is a stationary distribution of such a process. It is also shown that a stationary mode of the first-order autoregressive process possesses the stability property.