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

Limit formulas for the normalized fundamental matrix of the  northwest-corner truncation of Markov chains: Matrix-infinite-product-form  solutions of block-Hessenberg Markov chains