Level crossings and local time for regularized gaussian processes

• Autorzy: Berzin Corinne , León José R. , Ortega Joaquín
• Języki publikacji: EN

Abstrakty

EN

Let {X_t, t ∈[0, 1]} be a centred stationary Gaussian process defined on (Q, A, P) with со variance function satisfying r(t) ~ 1 — C|t|^2α, 0<α<l, as t→0. Define the regularized process X^ε = φ_ε * X_ε and Y^ε = X^ε/σ_ε, where σ<sup2</sup>_ε = varX^ε_t, is a kernel which approaches the Dirac delta function as ε→ 0 and * denotes the convolution. We study the convergence of [formula] where N^v(x) and L_v (x) denote, respectively, the number of crossings and the local time at level x for the process V in [0, 1] and..[formula] The limit depends on the value of α.

Słowa kluczowe

EN

gaussian processes; level crossings

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 1
• Strony: 39--81
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Berzin Corinne

• Université Paris XI, Laboratoire de Statistique Appliquée, Centre d’Orsay, Bat 425. 91405 Orsay Cédex

autor

León José R.

• Depto. de Matemáticas, Facultad de Ciencias, U.C.V., Apartado 47197, Caracas 1047, Venezuela

autor

Ortega Joaquín

• IVIC-Matemáticas, Apartado 21.827, Caracas 1020-A, Venezuela

Bibliografia

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