Mathematical notation of simulation question

Question

I would like to ask, what notation do you use, or how do you mathematically specify the following situation: I am simulating $n$ times random variable, where with probability $p$ it is $0$ and with probability $1-p$ it is $AR(2)$ process. What it is? It is somehow modified Bernoulli distribution, but I do not know how to correctly specify this simulation in my paper. Thank you for any help.

Answer 1

Just write $X_t=YZ_t$ where $Y\sim\operatorname{Bernoulli}(1-p)$ and $(Z_t)\sim AR(2)$. If you need $n$ of them just decorate with something like $X_t^{(i)}=Y^{(i)}Z_t^{(i)}$ or you have an $\mathbb{R}^n$-valued $AR(2)$?