Helen J. Wilson
An iterative scheme was introduced [Bradley, Dingle, Knottenbelt and Wilson, LAA 2003] using matrix-vector multiplication to calculate first passage times in semi-Markov processes. We show that the spectral radius of the matrix in question is at most 1, and prove that the method converges even when eigenvalues exist with modulus exactly 1. We also demonstrate correctness of the converged result.
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