  This paper considers the normalized fundamental matrix for the
northwest-corner (NW-corner) truncation of ergodic continuous-time Markov
chains, technically, of their infinitesimal generators. We first present a
limit formula for the normalized fundamental matrix of the NW-corner truncation
of the ergodic (infinitesimal) generator. The limit formula shows that, as the
order (size) of the NW-corner truncation diverges to infinity, the
corresponding normalized fundamental matrix converges to a stochastic matrix
whose rows are all equal to the stationary distribution vector of the ergodic
generator. Using the limit formula, we also derive the matrix-infinite-product
form (MIP-form) solutions of the stationary distribution vectors of upper and
lower block-Hessenberg Markov chains. In addition, from the MIP-form solutions,
we develop numerically stable and easily implementable algorithms that generate
the sequences of probability vectors convergent to the corresponding stationary
distribution vectors of block-Hessenberg Markov chains.
