$z_{n+1} = u_{n} * z_{n} + v_{n}$ stationary?

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I have the following question: When $u$ and $v$ are stationary processes, how can I show that $z_{n+1} = u_{n} * z_{n} + v_{n}$ is also stationary?

Obviously it looks like a AR(1) with time varying coefficient, but I don´t know how to show it.