Cammarota, V.; Lachal, A. Entrance and sojourn times for Markov chains, application to \((L, R)\)-random walks. (English) Zbl 1341.60086 Markov Process. Relat. Fields 21, No. 4, 887-938 (2015). Summary: In this paper, we provide a methodology for computing the probability distribution of sojourn times for a wide class of Markov chains. Our methodology consists in writing out linear systems and matrix equations for generating functions involving relations with entrance times. We apply the developed methodology to some classes of random walks with bounded integer-valued jumps. MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60G50 Sums of independent random variables; random walks 60J22 Computational methods in Markov chains Keywords:Markov chains; sojourn times; entrance times; \((L, R)\)-random walks; generating functions; matrix equations PDFBibTeX XMLCite \textit{V. Cammarota} and \textit{A. Lachal}, Markov Process. Relat. Fields 21, No. 4, 887--938 (2015; Zbl 1341.60086) Full Text: arXiv