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Convergence and Correctness of an Iterative Scheme for Calculating Passage Times in Semi-Markov Processes

Helen J. Wilson

Technical Report
Department of Applied Maths, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK
February, 2004
Volume 2004
Issue 1

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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