Asymptotic Behavior for Quadratic Variations of Non-Gaussian Multiparameter Hermite Random Fields

• Autorzy: Tran T. T. Diu

Identyfikatory

DOI

10.19195/0208-4147.39.2.8

• Języki publikacji: EN

Abstrakty

EN

Let (Z_t^q,H)_t∈[0,1]^d denote a d-parameter Hermite random field of order q ≥ 1 and self-similarity parameter H = (H₁,…, H_d) ∈ (1/2, 1)^d. This process is H-self-similar, has stationary increments and exhibits long-range dependence. Particular examples include fractional Brownian motion (q = 1, d = 1), fractional Brownian sheet (q = 1, d ≥ 2), the Rosenblatt process (q = 2, d = 1) as well as the Rosenblatt sweet (q = 2, d ≥ 2). For any q ≥ 2, d ≥ 1 and H ∈ (1/2, 1)^d we show in this paper that a proper renormalization of the quadratic variation of Z^q,H converges in L²(Ω) to a standard d-parameter Rosenblatt random variable with self-similarity index Hʺ = 1 + (2H − 2)/q.

Słowa kluczowe

EN

limit theorems; power variations; Hermite random field; Rosenblatt random field; self-similar stochastic processes

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 385--401
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Tran T. T. Diu

• Université du Luxembourg, UR en Mathématiques, 6, avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).