  In this work we survey on connections of Markov chains and the theory of
multiple orthogonality. Here we mainly concentrate on give a procedure to
generate stochastic tetra diagonal Hessenberg matrices, coming from some
specific families of multiple orthogonal, such as the ones of Jacobi--Pi\~neiro
and Hypergeometric Lima--Loureiro. We show that associated with a positive
tetra diagonal nonnegative bounded Hessenberg matrix we can construct two
stochastic tetra diagonal ones. These two stochastic tridiagonal nonnegative
Hessenberg matrices are shown to be, enlightened by the Poincar\'e theorem,
limit transpose of each other.
