Parham, G. A.; Soltani, A. R. Exact formulas for the moments of the first passage time of reward processes. (English) Zbl 1139.60340 REVSTAT 3, No. 1, 45-60 (2005). Summary: Let \(\{{\mathcal Z}_\rho(t), t\geq 0\}\) be a reward process based on a semi-Markov process \(\{{\mathcal J}(t), t\geq 0\}\) and a reward function \(\rho\). Let \(T_z\) be the first passage time of \(\{{\mathcal Z}_p(t), t\geq 0\}\) from \({\mathcal Z}_p(0)= 0\) to a prespecified level \(z\). In this article we provide the Laplace transform of the \(E[T^k_z]\) and obtain the exact formulas for \(ET_z\), \(ET^2_z\) and \(\text{var}(T_z)\). Formulas for certain type I counter models are given. Cited in 3 Documents MSC: 60K15 Markov renewal processes, semi-Markov processes 60E10 Characteristic functions; other transforms Keywords:semi-Markov process; reward process; Laplace transform; first passage time PDFBibTeX XMLCite \textit{G. A. Parham} and \textit{A. R. Soltani}, REVSTAT 3, No. 1, 45--60 (2005; Zbl 1139.60340)