# Name for this type of mixture of Markov chain?

Based on this paper, a mixture of Markov chains on a set $U$ is a $2$-tuple $(M,s)$ such that:

• $M$ is a set of $L$ Markov chains $\{M^1,\ldots,M^L\}$ on $U$(stochastic matrices such that $\sum_{y}M^i(x,y)=1)\ \forall x\in U,i\in\{1,\ldots,L\}$

• $s$ is a set of $L$ column vectors $\{s^1,\ldots,s^L\}$ of dimension $|U|\times 1$ such that $\sum_{i,x}s^i_x=1$

I'm looking for the name of mixture of Markov chains such that $\forall i,x:s^i_x>0$, as they are fully described by a function.