Endre Iglói

Karhunen-Loève expansions of α-Wiener bridges

AbstractWe study Karhunen-Loève expansions of the process(Xt(α))t∈[0,T) given by the stochastic differential equation % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX % garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wy % Ubqee0evGueE0jxyaibaieYdh9Lrpeeu0dXdh9vqqj-hEeeu0xXdbb % a9frpm0db9Lqpepeea0xd9q8as0-LqLs-Jirpepeea0-as0Fb9pgea % 0lrP0xe9Fve9Fve9qapdbaqaaeGaciGaaiaabeqaamaaeaqbaaGcba % acbaGaa8hzaiacyc4GybWaiGjGDaaaleacycOaiGjGdshaaeacycOa % iGjGcIcacWaMasySdeMaiGjGcMcaaaGccWaMaAypa0JamGjGgkHiTm % acyc4caaqaiGjGcWaMasySdegabGaMakacyc4GubGamGjGgkHiTiac % yc4G0baaaiacyc4GybWaiGjGDaaaleacycOaiGjGdshaaeacycOaiG % jGcIcacWaMasySdeMaiGjGcMcaaaGccGaSa+hzaiac8c4G0bGamWlG % gUcaRiac8c4FKbGaiGmGdkeadGaYaUbaaSqaiGmGcGaYaoiDaaqajG % mGaOGaiGmGcYcacGaGaInaaaWG0bGamaiGydaaayicI4SaiaiGydaa % ai4waiacaci2aaaaicdacGaGaInaaaGGSaGaiaiGydaaamivaiacac % i2aaaacMcaaaa!8F89!

Bispectral analysis of traffic in high-speed networks☆

dX_t^{(\alpha )} = - \frac{\alpha } {{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T)

Path Properties of Dilatively Stable Processes and Singularity of Their Distributions

, with the initial condition X0(α) = 0, where α > 0, T ∈ (0, ∞), and (Bt)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X(α). As applications, we calculate the Laplace transform and the distribution function of the L2[0, T]-norm square of X(α) studying also its asymptotic behavior (large and small deviation).

Bilinear Stochastic Systems with Long Range Dependence in Continuous Time

BackgroundImages 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.MethodsThis 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.ResultsDream 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 (χ2-test p value: 0.005). The content of images and dreams evoked using suggestions showed great agreement using all three anesthetic protocols.ConclusionThe 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.

Bilinear stochastic systems with fractional Brownian motion input

Abstract In this paper, we report results regarding bispectral analysis of the long range dependent ATM WAN traffic. Six different data sets were measured on 155 Mbps links of the SUNET by a custom-built tracing tool capable of recording over eight million consecutive cell arrivals. The complex fractal behavior of the ATM traffic claims utilization of the higher-order spectra analysis. For each of the analyzed data sets, it was found that the Gamma distribution fits very well. The bispectrum was studied for extracting some additional information with respect to the long memory parameter. The nonlinearity of the time series was also tested with the help of the bispectrum.

A rate-optimal trigonometric series expansion of the fractional Brownian motion.

The self-similar/multifractal nature of Internet traffic has been observed by several measurements and statistical studies. It has not been decided yet whether the traces are following either self-similar or multifractal flows. In this paper we analyzed Internet data traffic, both the classical Bellcore-data and data measured at our MAN by a local protocol analyzer. A new multifractal stochastic model was applied and showed its relevance in these cases.

Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

First, we present some results about the Hölder continuity of the sample paths of so-called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a corollary, we obtain that the most important (H, δ)-dilatively stable limit processes (e.g., the LISOU and the LISCBI processes, see [4]) almost surely have a local Hölder exponent H. Next we prove that, under some slight regularity assumptions, any two dilatively stable processes with stationary increments are singular (in the sense that their distributions have disjoint supports) if their parameters H are different. We also study the more general case of not having stationary increments. Throughout the article, we specialize our results to some basic dilatively stable processes such as the above-mentioned limit processes and the fractional Lévy process.

Karhunen-Loeve expansions of alpha-Wiener bridges

Application of a long range dependent model includes several fields of science and economics as geophysics, hydrology, turbulence, weather and so on. Recently it has been successfully used for modeling network traffic data (see [WTLW]). The basic stochastic process of this kind is the fractional Brownian motion defined in [MvN]. The fractional Brownian motion is given as a particular fractional operator on the standard Brownian motion. The linear or Gaussian parametric models of long range dependent phenomena are both the linear stochastic differential equations with fractional Brownian motion input and the fractional operator on the solution of a linear stochastic differential equation (see [C]). Actually these two types of processes are equivalent. Because most of the observations are not Gaussian there is a need nonlinear modeling of long range dependence. One possibility is to get rid of Gaussianity is the bilinear model started by Subba Rao [SR] in the discrete time case. The easy way to get a long range non-Gaussian process is to apply the fractional operator to the solution of the bilinear SDE. It is more painful to consider a bilinear SDE with fractional Brownian motion input.