We show that, under mild regularity conditions, the KKT conditions of the proposed model are necessary for local optimum.
Under mild regularity conditions, the asymptotic behavior of the local M-estimators for general weight functions is derived.
We obtain the leading asymptotic behaviour of HK1,K2 t) as t→0 under mild regularity conditions on K1 and K2.
We use this decomposition result to show that under mild regularity conditions, trajectory preserving maps between single-input affine control systems also lift trajectories.
Given an open-loop emissions strategy satisfying mild regularity conditions, an ambient transfer scheme is exhibited that induces it in Markov-perfect equilibrium (MPE).
Furthermore, under some mild regularity conditions, these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large.
Under mild regularity conditions, convergence to a local optimum is guaranteed if one uses an appropriate schedule for decreasing η towards 0 during learning [21].
We prove a concentration inequality which asserts that, under some mild regularity conditions, every random variable defined on the product of sufficiently many probability spaces exhibits pseudorandom behavior.
Remark 2.2 It is well known that (A4 - A7) are the mild regularity conditions for wavelet smoothing; see Antoniadis et al. [16], Chai and Xu [45], Xue [22], Sun and Chai [23], Zhou and You [46] and Li and Guo [24].
They gave an exact characterization of the distribution to which suitably scaled measures of instability converge have been defined, based on a sample drawn from any distribution in a satisfying mild regularity conditions.
