In this paper we study the additive functionals of Markov chains via conditioning with respect to both past and future of the chain. We shall point out new sufficient projective conditions, which assure that the variance of partial sums of n consecutive random variables of a stationary Markov chain is linear in n. The paper also addresses the central limit theorem problem and is listing several open questions.
Path independence of the additive functionals for McKean-Vlasov stochastic differential equations with jumps
Scaling limits of additive functionals of interacting particle systems
On the functional limits for sums of a function of partial sums
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