On some Limit Theorem for Markov Chain
Anna Czapkiewicz, Antoni Dawidowicz

TL;DR
This paper establishes conditions under which a central limit theorem holds for random variables governed by hidden Markov chains, specifically when the chain is ergodic and Lindeberg's condition is satisfied.
Contribution
It provides a proof that the CLT applies to hidden Markov chain-driven variables under ergodicity and Lindeberg's condition, extending existing results.
Findings
CLT holds for ergodic hidden Markov chains with Lindeberg's condition
Conditions identified that guarantee normal convergence of sums
Theoretical proof of CLT in this context
Abstract
The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables fullfiled Lindeberg's condition then the Central Limit Theorem is true.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Mathematical Dynamics and Fractals · Statistical Methods and Inference
