García-Mora, B.; Santamaría, C.; Rubio, G.; Pontones, J. L. Computing survival functions of the sum of two independent Markov processes: an application to bladder carcinoma treatment. (English) Zbl 1311.60084 Int. J. Comput. Math. 91, No. 2, 209-220 (2014). The framework of the paper is continuous time Markov processes on a finite discrete state space with all but one states transient and one absorbing state. The authors are concerned with the (random) time until absorption, the distribution of which is a phase-type (PH) distribution. In particular the authors calculate and compute the sum of two independent distributions of such type, which is again a phase-type distribution. The result is applied to study the evolution of bladder cancer based on a real data set. Reviewer: Martin Riedler (Wien) Cited in 3 Documents MSC: 60J27 Continuous-time Markov processes on discrete state spaces 60J28 Applications of continuous-time Markov processes on discrete state spaces 60J22 Computational methods in Markov chains 92C50 Medical applications (general) Keywords:Markov processes; phase-type distribution; bladder carcinoma PDFBibTeX XMLCite \textit{B. García-Mora} et al., Int. J. Comput. Math. 91, No. 2, 209--220 (2014; Zbl 1311.60084) Full Text: DOI References: [1] DOI: 10.1017/S0269964801153076 · Zbl 0982.62084 · doi:10.1017/S0269964801153076 [2] Graham A., Kronecker Products and Matrix Calculus with Applications (1981) · Zbl 0497.26005 [3] DOI: 10.3322/canjclin.50.1.7 · doi:10.3322/canjclin.50.1.7 [4] DOI: 10.1016/S0022-5347(01)67321-X · doi:10.1016/S0022-5347(01)67321-X [5] Jackson C., msm (Multi-state Markov and Hidden Markov Models in Continuous Time) [6] DOI: 10.1002/sim.886 · doi:10.1002/sim.886 [7] DOI: 10.1002/9781118032985 · doi:10.1002/9781118032985 [8] Kenny C.S., SIAM J. Matrix Anal. Appl 10 (3) pp 191– (1998) [9] Neuts M.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (1981) · Zbl 0469.60002 [10] DOI: 10.1007/978-3-642-59871-5 · doi:10.1007/978-3-642-59871-5 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.