Shi, Zhiyan; Yang, Weiguo; Tian, Lixin; Peng, Weicai A class of small deviation theorems for the random fields on an \(m\) rooted Cayley tree. (English) Zbl 1274.60101 J. Inequal. Appl. 2012, Paper No. 1, 15 p. (2012). Summary: In this paper, we are to establish a class of strong deviation theorems for the random fields relative to \(m\)th-order nonhomogeneous Markov chains indexed by an \(m\) rooted Cayley tree. As corollaries, we obtain the strong law of large numbers and Shannon-McMillan theorem for \(m\)th-order nonhomogeneous Markov chains indexed by that tree. Cited in 10 Documents MSC: 60F15 Strong limit theorems 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:strong deviation theorem; \(m\) rooted Cayley tree; \(m\)th-order nonhomogeneous Markov chain; Shannon-McMillan theorem PDFBibTeX XMLCite \textit{Z. Shi} et al., J. Inequal. Appl. 2012, Paper No. 1, 15 p. (2012; Zbl 1274.60101) Full Text: DOI References: [1] doi:10.1016/S0167-7152(03)00058-0 · Zbl 1116.60343 · doi:10.1016/S0167-7152(03)00058-0 [2] doi:10.1016/j.spl.2010.03.020 · Zbl 1196.60051 · doi:10.1016/j.spl.2010.03.020 [3] doi:10.1214/aop/1176988857 · Zbl 0793.60080 · doi:10.1214/aop/1176988857 [4] doi:10.1109/18.57200 · Zbl 0738.60100 · doi:10.1109/18.57200 [5] doi:10.1214/aop/1176989706 · Zbl 0760.05055 · doi:10.1214/aop/1176989706 [6] doi:10.1016/S0167-7152(00)00053-5 · Zbl 0981.60064 · doi:10.1016/S0167-7152(00)00053-5 [7] doi:10.1016/j.spl.2003.04.001 · Zbl 1068.60045 · doi:10.1016/j.spl.2003.04.001 [8] doi:10.1007/s11425-008-0015-1 · Zbl 1141.60011 · doi:10.1007/s11425-008-0015-1 [9] doi:10.1109/TIT.2004.838339 · Zbl 1319.60066 · doi:10.1109/TIT.2004.838339 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.