On the CLT for additive functionals of Markov chains
نویسندگان
چکیده
منابع مشابه
An Invariance Principle for the Law of the Iterated Logarithm for Additive Functionals of Markov Chains
In this paper, we prove Strassen’s strong invariance principle for a vector-valued additive functionals of a Markov chain via the martingale argument and the theory of fractional coboundaries. The hypothesis is a moment bound on the resolvent.
متن کاملThe Law of the Iterated Logarithm for Additive Functionals of Markov Chains
In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M. Maxwell and M. Woodroofe [7] (2000). The main technique is the martingale argument and the theory of fractional coboundaries.
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We prove an invariance principle for a vector-valued additive functional of a Markov chain for almost every starting point with respect to an ergodic equilibrium distribution. The hypothesis is a moment bound on the resolvent.
متن کاملAn Almost Sure Invariance Principle for Additive Functionals of Markov Chains
In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M. Maxwell and M. Woodroofe [7] (2000). The main technique is the martingale argument and the theory of fractional coboundaries.
متن کاملUniform CLT for Markov chains with a countable state space
Let (S,G, P ) be a probability space and let F be a set of measurable functions on S with an envelope function F finite everywhere. Let X1, X2, ... be a strictly stationary sequence of random variables with distribution P , and define the empirical measures Pn, based on {Xi}, as Pn = n−1 ∑n i=1 δXi . We say the uniform CLT holds over F , if n 1 2 (Pn − P ) converges in law, in the space l∞(F ) ...
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2020
ISSN: 1083-589X
DOI: 10.1214/20-ecp318