CLT in the perturbative regime Sample Clauses

CLT in the perturbative regime. In the context of Section 2.3, the proof of Theorem 3.2 does not need the machinery of the previous section. Indeed, as we pointed out in (2.104), Xt − vt can be decomposed as a sum of a martingale (Mt)t≥0 and an additive functional of the environment process (ηt)t≥0, i.e., Xt − vt = Mt + (α − β) ∫ t ( 2ηs(0) − 1) ds − vt = Mt + ∫ ƒ (ηs)ds. (3.50) In the spirit of Kipnis-Varadhan [61], we would like to write the additive functional in (3.50) as the sum of a martingale (Mt')t≥0 plus a term (ϵt)t≥0 that is negligible when we