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- W77729304 abstract "Frakcionalis Ornstein-Uhlenbeck lepedő tulajdonsagait vizsgaltuk abbol a szempontbol, hogy olyan modellt konstrualjunk, aminek spektruma az origo kornyezeteben nem izotrop modon viselkedik. A Levy-Flight-ok (kozel stabilis Levy-folyamtok) fontos szerepet jatszanak a nem Gauss jelensegek vizsgalataban. Egzakt eredmenyeket bizonyitottunk a Levy-Flight-ok aszimptotikus egesz es tort rendű momentumaira, ezzel osszefuggesben sikerult kimutatni ezek multi-fraktal tulajdonsagat. A nemlinearis vektor ertekű regresszio problemajaval foglalkoztunk, amikor a megfigyelesek hibaja stacionarius eloszlasu. Egzakt formulat adtunk meg a parameter becslesek aszimptotikus szorasmatrixara, es alkalmaztuk eredmenyunket valodi adatokra is. A magfuggvenyes sűrűsegfuggveny becsles aszimptotikus normalitasat bizonyitottuk ugy, hogy a mezőt egyre nagyobb tartomanyon figyeljuk meg, de kozben megfigyelesi helyeket is sűritjuk. Kiderul, hogy az aszimptotikus kovariancia fugg a savszelesseg es az osztopontok tavolsaganak aranyatol. | The Fractional Ornstein-Uhlenbeck sheet is investigated, non-isotropic stationary model is constructed and applied for real data. We showed that Levy-Flights are fractals and proved asymptotical formulae for moments and cumulants.with integer and fractal order. Functional limit theorems are proved for a sequence of Galton-Watson processes with immigration, where the offspring mean tends to its critical value 1 under weak conditions for the variances of offspring and immigration processes. Int he limit theorems the norming factors depend on these variances. We proved the asymptotic normality of the kernel density estimates in 2D. The asymptotic covariance is shown to be dependent of the ratio of the window size and distance between point on the lattice. The nonlinear multiple regression with stationary errors is investigated. A clear formula is given for the asymptotic variance of the parameter estimator and it is applied for the identification of fitting models to real data." @default.
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- W77729304 date "2008-01-01" @default.
- W77729304 modified "2023-09-25" @default.
- W77729304 title "Idősorok analízise és sztochasztikus fraktál modellek tanulmányozása alkalmazásokkal = Time series analysis and fractal models with applications" @default.
- W77729304 hasPublicationYear "2008" @default.
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