On the rate of convergence to the normal law for solutions of the burgers equation with singular initial data

Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long‐range dependence

“…For this, we have to replace condition C by a more general condition which can be given in the spectral form, such as (21), together with the type of results of Lemma 4.5 and a precise behavior of the spectral density near infinity (for example, f(A) O(]A[ -1-a) as ])[--OO). Then, instead of the convolution property (22), we may use the Riesz Composition Formula (see Lemma 4.6 below) for an investigation of the asymptotic behavior of convolutions of spectral density. Lemma 4.2 can next be used again to obtain the asymptotic formulae similar to (9) but in terms of the spectral density.…”