On the functional central limit theorem for stationary processes

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Necessary and sufficient conditions for the conditional central limit theorem (2002, methodology): “Now arguing as in Claim 1(b) in Dedecker and Rio (2000), we obtain E(E(|Sn||M0)|I) = E(|Sn||I).”
A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics (2013, methodology): “Under projective conditions, versions of a CLT were derived by Dedecker [9], Dedecker and Rio [11] and Dedecker and Merlevède [10].”
Coupling for τ-Dependent Sequences and Applications (2004, background): “Dedecker and Rio(12) have proved that for any Markov chain belonging to ARL(C, δ, S), there exists an unique invariant probability μ, and that μ(|x|S−δ) <∞.”
The conditional central limit theorem in Hilbert spaces (2003, background): “…− GN : Write ;rst∣∣∣∣∣ ∣∣∣∣∣ i; j(N )− E ( 1 n n∑ k=1 n∑ ‘=1 Zk; iZ‘; j|M0 )∣∣∣∣∣ ∣∣∣∣∣ 1 6 ∣∣∣∣∣ ∣∣∣∣∣ i; j(N )− E ( 1 n ∑ GN Zk; iZ‘; j|M0 )∣∣∣∣∣ ∣∣∣∣∣ 1 + 1 n ∣∣∣∣∣∣ ∣∣∣∣∣∣ ∑ RGN E(Zk; iZ‘; j|M0) ∣∣∣∣∣∣ ∣∣∣∣∣∣ 1 : (3.38) From Claim 1(a) in Dedecker and Rio (2000), we know that i; j(N ) = E( i;…”