Let (x_n)_(n≥0) be a digital (t, s)-sequence in base 2, P_m = (X_n)_(n=0~(2~m-1)), and let D(P_m, Y) be the local discrepancy of P_m. Let T ⊕ Y be the digital addition of T and Y. and let M_(s,p)(_Pm) = ( ∫ |D(P_m⊕r,y)|~pdrdv)~(1/p). [0,1)~(2s) In this paper, we prove that D(P_m ⊕ T, Y)/M_(s,2)(P_m) weakly converges to the standard Gaussian distribution for m→∞, where T, Y are uniformly distributed random variables in [0, 1)~s. In addition, we prove that M_(s,2)(P_m)/M_(s,2)(P_m)→1/[(2π)~(1/2) ]∞∫-∞ |u|~(p_e-u~2/2)du for m → ∞, p > 0.
展开▼
