The CLT for Markov chains with a countable state space embedded in the space lp

Tsung-Hsi Tsai

Stochastic Processes and their Applications, 2001, vol. 91, issue 1, 39-46

Abstract: We find necessary and sufficient conditions for the CLT for Markov chains with a countable state space embedded in the space lp for p[greater-or-equal, slanted]1. This result is an extension of the uniform CLT over the family of indicator functions in Levental (Stochastic Processes Appl. 34 (1990) 245-253), where the result is equivalent to our case p=1. A similar extension for the uniform CLT over a family of possibly unbounded functions in Tsai (Taiwan. J. Math. 1(4) (1997) 481-498) is also obtained.

Keywords: Markov; chains; CLT; Empirical; processes; Regenerative; processes (search for similar items in EconPapers)
Date: 2001
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