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Strong ratio limit property for ๐‘…-recurrent Markov chains

Strong ratio limit property for ๐‘…-recurrent Markov chains

for some positive integer d, then SRLP holds. It is also shown that the inequality (1.2) is always satisfied in a reversible chain. When R = 1, the results given here reduce to those of Orey [7 ] for recurrent chains, while for R > 1 they imply SRLP for โ€ฆ