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.