作者：Forman, Noah; Rizzolo, Douglas; Shi, Quan; Winkel, Matthias
作者单位：McMaster University; University of Delaware; University of Mannheim; University of Oxford
摘要：We give a pathwise construction of a two-parameter family of purelyatomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson-Dirichlet(alpha,theta) distributions, for alpha is an element of(0, 1) and theta >= 0. These processes resolve a conjecture of Feng and Sun (Probab. Theory Related Fields 148 (2010) 501-525). We build on our previous work on (alpha, 0)- and (alpha, alpha)-interval partition evolutions. The extension to general theta >= 0 is achieved...
作者：Hager, Paul; Neuman, Eyal
作者单位：Humboldt University of Berlin; Imperial College London
摘要：We consider a family of fractional Brownian fields {B-H} H is an element of(0,1) on R-d, where H denotes their Hurst parameter. We first define a rich class of normalizing kernels psi and we rescale the normalised field by the square-root of the gamma function Gamma(H), such that the covariance of X-H (x) = Gamma(H)(1/2) (B-H(x)- integral(Rd) B-H (u)Psi(u, x) du), converges to the covariance of a log-correlated Gaussian field when H down arrow 0. We then use Berestycki's good points approach (...
