Proposition 7.9 . [0568] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Proposition 7.9 .
On the intersection 𝐈𝐈 − ∩ 𝐈𝐈𝐈 − ∩ X ^ t {\bf{II}_{-}}\cap{\bf{III}_{-}}\cap\widehat{X}_{t} k ≥ 0 k\geq 0
(7.137) | ∇ k ( ϕ t , 𝐈𝐈 − − η 1 ) | = O ( e − δ e T ) , |\nabla^{k}(\phi_{t,\bf{II}_{-}}-\eta_{1})|=O(e^{-\delta_{e}T}),
where the derivative and norm are taken with respect to ω ( t ) \omega(t) δ e \delta_{e} 4.23