Jin, Shaohua; Peng, Xiaoli A strong deviation theorem for non-homogeneous Markov chain on a non-homogeneous tree. (Chinese. English summary) Zbl 1424.60026 Acta Anal. Funct. Appl. 20, No. 2, 150-156 (2018). Summary: In recent years, tree-indexed stochastic processes have become one of the hot topics in probability theory. The strong deviation theorem is one of the central issues of probability theory. In this paper, applying Doob’s martingale convergence theorem, a strong deviation theorem on the generalized gambling system for \(m\)-ordered non-homogeneous Markov chain on a non-homogeneous tree is given. MSC: 60F10 Large deviations 60F15 Strong limit theorems 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:non-homogeneous tree; Markov chain; martingale; sample divergence; generalized gambling system; strong deviation theorem PDFBibTeX XMLCite \textit{S. Jin} and \textit{X. Peng}, Acta Anal. Funct. Appl. 20, No. 2, 150--156 (2018; Zbl 1424.60026) Full Text: DOI