Mario Lefebvre, "A First-Passage-Time Problem for a Discrete-Time Markov Process," International Journal of Applied Mathematics, Computational Science and Systems Engineering, vol. 6, pp. 76-81, 2024, DOI:10.37394/232026.2024.6.7
Mario Lefebvre. A First-Passage-Time Problem for a Discrete-Time Markov Process.
International Journal of Applied Mathematics, Computational Science and Systems Engineering. 2024;6:76-81. 10.37394/232026.2024.6.7
International Journal of Applied Mathematics, Computational Science and Systems Engineering
E-ISSN: 2766-9823
Volume 6, 2024
A First-Passage-Time Problem for a Discrete-Time Markov Process
Author:
Abstract: We consider the discrete-time stochastic process $$\lbrace X_{n}, n = 0, 1, . . .\rbrace$$ defined by $$X_{n+1} = X_{n} − ϵ_{n+1}$$,
where $$ϵ_{n+1}$$ is a non-negative random variable. The aim is to compute the mean first-passage time to zero for this
process, which can be used as a model for the remaining lifetime of a machine. Particular cases are solved exactly
and explicitly.
Pages: 76-81 DOI: 10.37394/232026.2024.6.7WSEAS Transactions on International Journal of Applied Mathematics, Computational Science and Systems Engineering, E-ISSN: 2766-9823, Volume 6, 2024, Art. #7
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