Idősorok analízise és sztochasztikus fraktál modellek tanulmányozása alkalmazásokkal = Time series analysis and fractal models with applications

Frakcionális Ornstein-Uhlenbeck lepedő tulajdonságait vizsgáltuk abból a szempontból, hogy olyan modellt konstruáljunk, aminek spektruma az origó környezetében nem izotróp módon viselkedik. A Lévy-Flight-ok (közel stabilis Lévy-folyamtok) fontos szerepet játszanak a nem Gauss jelenségek vizsgálatában. Egzakt eredményeket bizonyítottunk a Lévy-Flight-ok aszimptotikus egész és tört rendű momentumaira, ezzel összefüggésben sikerült kimutatni ezek multi-fraktál tulajdonságát. A nemlineáris vektor értékű regresszió problémájával foglalkoztunk, amikor a megfigyelések hibája stacionárius eloszlású. Egzakt formulát adtunk meg a paraméter becslések aszimptotikus szórásmátrixára, és alkalmaztuk eredményünket valódi adatokra is. A magfüggvényes sűrűségfüggvény becslés aszimptotikus normalitását bizonyítottuk úgy, hogy a mezőt egyre nagyobb tartományon figyeljük meg, de közben megfigyelési helyeket is sűrítjük. Kiderül, hogy az aszimptotikus kovariancia függ a sávszélesség és az osztópontok távolságának arányától. | The Fractional Ornstein-Uhlenbeck sheet is investigated, non-isotropic stationary model is constructed and applied for real data. We showed that Lévy-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

The effect of preoperative suggestions on perioperative dreams and dream recalls after administration of different general anesthetic combinations: a randomized trial in maxillofacial surgery

Background Images evoked immediately before the induction of anesthesia with the help of suggestions may influence dreaming during anesthesia.The aim of the study was to assess the incidence of evoked dreams and dream recalls by employing suggestions before induction of anesthesia while administering different general anesthetic combinations. Methods This is a single center, prospective randomized including 270 adult patients scheduled for maxillofacial surgical interventions.Patients were assigned to control, suggestion and dreamfilm groups according to the psychological method used. According to the anesthetic protocol there were also three subgroups: etomidate & sevoflurane, propofol & sevoflurane, propofol & propofol groups. Primary outcome measure was the incidence of postoperative dreams in the non-intervention group and in the three groups receiving different psychological interventions. Secondary endpoint was to test the effect of perioperative suggestions and dreamfilm-formation training on the occurrance of dreams and recallable dreams in different general anesthesiological techniques. Results Dream incidence rates measured in the control group did not differ significantly (etomidate & sevoflurane: 40%, propofol & sevoflurane: 26%, propofol & propofol: 39%). A significant increase could be observed in the incidence rate of dreams between the control and suggestion groups in the propofol & sevoflurane (26%-52%) group (p = 0.023). There was a significant difference in the incidence of dreams between the control and dreamfilm subgroup in the propofol & sevoflurane (26% vs. 57%), and in the propofol & propofol group (39% vs.70%) (p = 0.010, and p = 0.009, respectively). Similar to this, there was a significant difference in dream incidence between the dreamfilm and the suggestion subgroups (44% vs. 70%) in the propofol & propofol group (p = 0.019). Propofol as an induction agent contributed most to dream formation and recalls (chi2-test p value: 0.005). The content of images and dreams evoked using suggestions showed great agreement using all three anesthetic protocols. Conclusion The psychological method influenced dreaming during anesthesia. The increase of the incidence rate of dreams was dependent on the anesthetic agent used, especially the induction agent. The study was registered in ClinicalTrials.gov. Identifier: NCT01839201

Renormalization group of and convergence to the LISDLG process

The LISDLG process denoted by J(t) is defined in Iglói and Terdik [ESAIM: PS 7 (2003) 23–86] by a functional limit theorem as the limit of ISDLG processes. This paper gives a more general limit representation of J(t). It is shown that process J(t) has its own renormalization group and that J(t) can be represented as the limit process of the renormalization operator flow applied to the elements of some set of stochastic processes. The latter set consists of IGSDLG processes which are generalizations of the ISDLG process

Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance and validation of the proposed model are demonstrated by real data of Internet traffic.