Manuscript Psy02-A@1 · Psy02-A.tex · section · d92ce402

Delayed product realization and robustness

A separate normalization-independent response benchmark › Delayed product realization and robustness · lines 1855–1879

For an explicit allowance, suppose the relative tests have time support in $[d, T]$ , $0 < d < T$ . Define a $C^{1}$ seminorm using the supremum of the test and its spatial gradient. Equation (eq:finite-part) gives

\abs ⟨ R, G ⟩ \leq C_{d, T} \norm G_{C^{1}}, C_{d, T} = \abs γ π (lo g (T / d) + T - d),

for tests with this time support. Taylor's theorem gives

\norm F_{f, h_{δ}} - f_{C^{1}} \leq δ \norm f_{C^{2}},

where the $C^{2}$ seminorm includes the gradient and Hessian bounds needed for translations.

Displayed formulas in this passage

unlabeled · line 1862
$\abs ⟨ R, G ⟩ \leq C_{d, T} \norm G_{C^{1}}, C_{d, T} = \abs γ π (lo g (T / d) + T - d),$
unlabeled · line 1873
$\norm F_{f, h_{δ}} - f_{C^{1}} \leq δ \norm f_{C^{2}},$

Delayed product realization and robustness

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