It's been several weeks since my attempts to work with Matrix Stochastic Recurrence Equations. I have founded a lot of references, books and recent works about Stochastic Recurrence Equations in time series and stochastic processes, usually with applications to GARCH Processes.
Loosely speaking, these works consider the general SRE \begin{equation} X_t = A_t X_{t-1} + B_t \end{equation} where $X_t \in \mathbb{R}^N$ is a vector-valued stochastic process, $A_t \in \mathbb{R}^{N\times N}$ and $ B_t\in \mathbb{R}^N$.
My question is, what if I want to study a matrix-valued stochastic process, for example, $\boldsymbol{X}_t \in \mathbb{R}^{N \times N^2}$, $\boldsymbol{A}_t \in \mathbb{R}^{N \times N}$ and $\boldsymbol{B}_t \in \mathbb{R}^{N \times N^2}$ ?
