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Numerical Computation of the Rosenblatt Distribution and Applications

Year: 2025
Type: article
Abstract: ABSTRACT The Rosenblatt distribution plays a key role in the limit theorems for non‐linear functionals of stationary Gaussian processes with long‐range dependence. We derive new expressions for the characteristic function of the Rosenblatt distribution. Also we present a novel accurate approximation of all eigenvalues of the Riesz integral operator associated with the correlation function of the Gaussian process and propose an efficient algorithm for computation of the density of the Rosenblatt distribution. We perform Monte‐Carlo simulation for small sample sizes to demonstrate the appearance of the Rosenblatt distribution for several functionals of stationary Gaussian processes with long‐range dependence.
Source: Stat
DOI: 10.1002/sta4.70107
Institution: Cardiff University
Language: English
Open Access status: hybrid
Estimated APC paid: $3,610
Funders: Cardiff University, Fundação de Amparo à Pesquisa do Estado de São Paulo, Hrvatska Zaklada za Znanost, Engineering and Physical Sciences Research Council, Australian Research Council, Division of Mathematical Sciences
Awards: Isaac Newton Institute for Mathematical Sciences (INI), G2203179303, Random fields: non-Gaussian stochastic models and approximation schemes, Fractional differential systems and stochastic, G3341554066, Isaac Newton Institute for Mathematical Sciences, Scaling in stochastic models
OpenAlex ID: W4415686483
FWCI: 0.83
Cites: 22
Cited by: 1
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