Let's consider stochastic recurrence equation (SRE) $Y_t = A_t Y_{t-1} + B_t $ where $(A_t)_{t\in \mathbb{Z}}$, $(B_t)_{t\in \mathbb{Z}}$ are sequences of iid random variables. I've found in some books and articles the following theorem:
If $\mathbb{E} (\ln |B_t|)^+ < \infty $ and $\mathbb{E}(\ln |A_t|)<0 $ then (SRE) has unique and stationary solution given by \begin{equation} Y_t = B_t + \sum_{i=1}^{\infty} B_{t-i} \prod_{j=0}^{i-1} A_{t-j} \end{equation}
While I've found definition of stationarity (both weak and string) of stochastic process, I can't find explicite definition of stationary solution to stochastic equation. Does the stationarity of solution mean that the process given by formula in theorem is just a stationary process?