Normal Approximation by Stein’s Method

AR(1) processes driven by second-chaos white noise: Berry–Esséen bounds for quadratic variation and parameter estimation

“…A straightforward computation shows that under Assumption (9), the kernel f i ∈ L 2 ([0, 1] 2 ) for all i 1 : indeed…”

Rate of convergence in the Breuer-Major theorem via chaos expansions

“…Stein's method. We refer to [6] for a complete presentation of this topic. Let h : R → R be a Borel function such that h ∈ L 1 (R, γ).…”

“…Changing the exponents β jk + 1 in to β jk for (j, k) ∈ {(1, 2), (1,3), (1,4), (5,6), (5, 7), (5, 8)}, we can write…”

“…The exponents β jk induce an unordered simple graph on the set of vertices V = {1, 2, 3, 4, 5, 8} by putting an edge between j and k whenever β jk = 0. Because β 12 , β 13 ≥ 1, β 14 ≥ 1, β 56 ≥ 1, β 57 ≥ 1 and β 58 ≥ 1, there are edges connecting the pairs of vertices (1, 2), (1,3), (1,4), (5,6), (5,7) and (5,8). Condition (5.10) means that the degree of each vertex is at least 2.…”

“…1≤k<l≤8 β kl ! and D (2) q = {(β kl ) 1≤k<l≤8 : k or l=j β kl = q j − 1 for j = 3, 4, 7, 8and k or l=j β kl = q j − 2 for j = 1, 2, 5, 6}.Changing the exponents β jk + 1 in to β jk for (j, k) ∈ {(1, 2), (1, 3), (2, 4),(5,6),(5,7),(6|c q j |(q j − 1)! (β 12 − 1)!…”