NOVEL AND FASTER WAYS FOR SOLVING SEMI-MARKOV PROCESSES

NOVEL AND FASTER WAYS FOR SOLVING SEMI-MARKOV PROCESSES

MATHEMATICAL AND NUMERICAL ISSUES

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Semi-Markov processes (SMP) are powerful stochastic tools for modeling reliability measures over time. This work precisely aims at proposing more efficient mathematical and numerical treatments for SMP in continuous time. The first approach (called 2N-) is based on transition frequency densities and general quadrature methods. The other proposed method (in short Lap-) applies Laplace transforms that are inverted by a Gaussian quadrature method known as Gauss Legendre to obtain the state probabilities in time domain. Mathematical formulation of these approaches as well as descriptions of their ...