B. Mandelbrot and J. W. V. Ness, "Fractional Brownian motions, fractional noises and applications, " SIAM Review, vol. 10, pp. 422--437, Oct. 1968.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....interfaces or from LSPs in Multiprotocol Label Switching (MPLS) networks. The vast literature on characteristics of network traffic based on detailed packet trace data provides strong evidence that different types of traffic on high speed data networks are selfsimilar, so the Hurst parameter [11] which describes long range dependence, remains the same for different levels of aggregation. These include studies of Local Area Network traces [9] Wide Area Network traffic [12] and variable bit rate traffic [1] Crovella and Bestavros [2] provided an example in which the estimated Hurst ....

.... with parameter if for any and any # ( # ) 0 1 2 ( 3 54 where the notation # 6 , 879 # 3 means that the two processes # 87: 3 have the same finite joint distributions [11]. The self similarity parameter is also called Hurst parameter. Fractional Brownian motion (fBm) is the unique self similar Gaussian process so it makes a natural choice for a model of cumulated traffic. Increments of an fBm process are known as fractional Gaussian noise (fGn) which is the ....

Mandelbrot, B. B. and van Ness, J. W., "Fractional Brownian motions, fractional noises and applications," SIAM Review, vol. 10, pp. 422-37, 1968.

....some others properties, particularly paths properties, and give easily simulation algorithms of such of fields. INTRODUCTION Ce papier est le d eveloppement d une note aux CRAS [7] dont l objet est une g en eralisation du mouvement brownien fractionnaire d efini par Mandelbrot et Van Ness(1968) [10] aux champs al eatoires d efinis comme double int egrale fractionnaire d un bruit blanc [9] et index e par deux param etres ff et fi. Contrairement au champ brownien fractionnaire [9] ou encore au champ brownien fractionnaire de L evy [3] le drap brownien fractionnaire que nous avons d efini ....

....l int egrand appartient a L . Or : ff (s; u)f fi (t; v)dudv = fi (t; v)dv) Comme f ff et f fi sont les int egrands d un mouvement brownien fractionnaire (aux constantes pr es) de param etre respectif ff et fi, on obtient les memes conditions que dans le cas a un indice ([10]) Donc W ff;fi est bien d efini d es que ff 2]0; 1[ et fi 2]0; 1[ 2 Proposition 2 Le champ W ff;fi est un champ al eatoire gaussien centr e nul sur les axes. Preuve : Soit ff; fi 2]0; 1[ W ff;fi est un processus gaussien. En effet, pour tout n 0; 8(x 1 ; x n ) 2 R , et 8( s 1 ; t ....

B.B. Mandelbrot, J.W. Van Ness, "Fractional Brownian motion , Fractional noises and applications", SIAM Review 10, 422-437, 1968.

.... 2; g fz 2 C ; Argj1 zj g of the power series 1 k=0 ( k ( k ( k k z : 15) Here ( k is de ned by (a) 0 = 1 and (a) k (a k) a) a(a 1) a k 1) 10 Note that W is more widely used in applications than B because it has stationary increments (see [3, 8] for some other features of B ) in fact the covariance kernel of W is given by : s W def (s t jt sj ) where, 2 2H) cos( H) H(1 2H) It has been shown in [3] that for any regular f; we have ) E (t; s)u s dB s ; where u is a progressively ....

Mandelbrot, B. and J. Van Ness: 1968, `Fractional Brownian Motions, Fractional Noises and Applications'. SIAM Review 10(4), 422437.

....video traffic and see how they influence the queue length distribution. 2. Traces description The traces were generated by implementing the usual discretization of the so called harmonizable representation of fractional brownian motion (FBM) i.e. discrete time Fractional Gaussian Noise (dFGN) [3]. Here we skip all technical details and just say that the harmonizable representation of FBM consists of writing it as a weighted average of its past values, where the weights are given by a memory kernel which decays to zero as you look further away into the past. We refer the reader to [1] ....

B. B. Mandelbrot and J. W. Van Ness, "Fractional Brownian motions, fractional noises and applications", SIAM Review, vol. 10, pp. 422-437, 1998

....using MATLAB on a Sun workstation with a oating point precision of approximately 2 10 16 . 5.1. Fractional Brownian Motion The rst example consists of simulating and approximating the covariance matrix of 1024 samples of a fractional Brownian motion (fBm) with a Hurst parameter H = 3=4 [13]. The covariance of fBm is given by K xx (s; t) 1 2 jtj 2H jsj 2H jt sj 2H : 29) Note that fBms have stationary increments, and one can synthesize this fBm exactly with 2048 point FFTs and also generate good nite rank approximations to the covariance matrix, as discussed in ....

Mandelbrot, B. B. and J. W. V. Ness: 1968, `Fractional Brownian Motions, Fractional Noises and Applications'. SIAM Review 10(4), 422-437.

....D 1 (see Table 1) In this case, the amplitude distribution does not converge to a Gaussian form, and in particular the associated mean and variance are infinite. This fractal shot noise process should be contrasted with fractional Brownian motion (FBM) developed by Mandelbrot and Van Ness [15, 16]. Fractional Brownian motion usually has a Gaussian amplitude distribution, but the times between zero crossings have a L evy stable time interval distribution. Our L evy stable process, in contrast, has a L evy stable amplitude distribution and no zero crossings. In addition, the fractal nature ....

....P (I) converges to the Gaussian density for arbitrary B since the area under the impulse response function and under its square are both finite. The L evy stable shot noise process developed here is fundamentally different from fractional Brownian motion (FBM) developed by Mandelbrot and Van Ness [15, 16]. FBM has an amplitude distribution determined by the increments in its definition, and may have any amplitude distribution, although FBM is usually Gaussian. For Gaussian FBM the times between level crossings exhibit a L evy stable time distribution with dimension between 0 and 1. Our ....

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B. B. Mandelbrot and I. W. Van Ness, "Fractional Brownian motions, fractional noises, and applications," Soc. for Ind. and Appl. Math. (SIAM) Review, vol. 10, pp. 422-437, 1968

....would tend to be smoothed by averaging over a long enough time scale. However, measurements of real VBR traffic indicate that significant traffic burstiness is present on a wide range of time scale [Beran, 1995 ] An example of the self similar stochastic model is the fractional Gaussian noise [Mandelbrot,1968]. In the next chapter, we will present a simulation system for Virtual U, a networked learning system. 24 Chapter III The Simulation System 3.1 Overview The goals of our work are to build a simulation system that can represent a real telelearning environment and to carry out research on ....

B. Bl Mandelbrot and J. W. Van Ness, "Fractional Brownian Motions, Fractional Noises and Applications," SIAM Review, vol. 10, 1968.

....and simulation investigations of the effects of different non stationarity phenomena in the data. The issue is not new and also addressed in the hydrology literature (e.g. 9] after the application of LRD processes in the modeling of natural storage systems by Hurst [7] Mandelbrot and others [11]. However, after the invent and first application of LRD processes in the teletraffic research a number of papers have been published just by blind application of some LRD tests assuming the stationarity for hours of the traffic and taking no The research was supported by the Inter University ....

B.B. Mandelbrot and J.W. Van Ness, "Fractional Brownian Motions, Fractional Noises and Applications," SIAM Rev., vol. 10, pp. 422--437, 1968.

....as industrial production and commodity price indexes, suggested overwhelming importance of the low frequency components. 84]observed a self similar behaviour in the distribution of speculative prices, and proposed continuous and discrete time fractional models, such as fractional Brownian motion [85]. He then developed the Hurst rescaled range (hereafter R S) analysis, originally introduced in [83] for social measurement purposes. However, initial sizeable empirical success of the long range dependence (LRD) concept in economics is certainly related to the autoregressive fractionally ....

Mandelbrot, B. B., and J. W. V. Ness (1968): "Fractional Brownian motions, fractional noise and applications," SIAM Review, 10, 422--437. 1. The Long Range Dependence Paradigm for Macroeconomics and Finance 21

....to these cases by differencing the process. In this paper we restrict ourselves to the stationary long memory case because this is the relevant situation in practise. 2. 2 Modeling long memory processes A first model for long memory processes was the fractional Brownian motion introduced by Mandelbrot van Ness (1968). This approach generalizes standard Brownian motion by using self similar processes. Here a process X t is called self similar with parameter d 2 ( Gamma1=2; 1=2) if X t D = t d X 1 . Notice that these equality is only equality in distribution. Self similarity is not a property of the paths ....

Mandelbrot, B. B., van Ness, J. W. (1968): "Fractional Brownian motions, fractional noises and applications." SIAM Review 10, 422 - 437.

....Work carried out while supported by NSF Postdoctoral Fellowship Grant DMS 9508709 at IBM T.J. Watson Research Center, New York, and Department of Industrial Engineering and Operations Research, Columbia University, New York. 1 1 Introduction It is well known, following Mandelbrot and van Ness [19], that the fractional Brownian motion (FBM) denoted BH (with BH (0) 0) relates to the standard Brownian motion, B, through the following integral relation: BH (t) 1 Gamma(H 1 2 ) Delta f Z t 0 (t Gamma s) H Gamma1=2 dB(s) Z 0 Gamma1 [ t Gamma s) H Gamma1=2 Gamma ....

....work, Chang, Yao, and Zajic [7] Also refer to [8] which is part of the proceedings of an international workshop on stochastic networks, where an early version of some of our results were previewed. In [7] our starting point was an alternative FBM model, due to L evy ( 18] also refer to [19]) BH (t) 1 Gamma(H 1 2 ) Delta Z t 0 (t Gamma s) H Gamma1=2 dB(s) 2) We used the integral relation in (2) as a basic filter . Indeed, in (2) the FBM can be viewed as the output of a time invariant linear filter with the impulse response h(t) t H Gamma1=2 subject to an ....

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B.B. Mandelbrot and J. van Ness, "Fractional Brownian motions, fractional noises and applications," SIAM Review, Vol. 10, No. 4, pp. 422-437, 1968.

....classes of computer generated fractal images whose complexity (dimension) is known and could be varied in a highly controlled manner. The fractal images for this experiment were generated using the mathematical model of fractional Brownian motion (fBm) defined by Mandelbrot and Van Ness. [10] [11] The resulting Brownian motion, or random walk, was projected onto a Cartesian plane with an associated magnitude at every position. The advantage of using this algorithm is that for different random number generator seed values different images may be generated, all having the same fractal ....

....is given by: D = 3 H 7 This filtering method uses a Gaussian density function to give the desired spectral characteristic. The transformation has a Gaussian exponential dependence which is achieved via the sum of n independent identically distributed random variables (pseudorandom numbers) [10] By virtue of the central limit theorem, as n approaches infinity, the distribution tends toward normal. The spectral components are generated first in their polar coordinate representation. The spectral elements are the complex values in the fractal object array. With the polar coordinate ....

B. B. Mandelbrot and J. W. Van Ness, "Fractional Brownian Motion, Fractional Noises and Applications", SIAM Review, vol. 10, no. 4, 1968, pps 422-437.

....spectrum P (w) oe 2 jwj 2ff 1 ; where oe is a positive constant and 0 ff 1. The realizations of a fBm are singular almost everywhere and are statistically self similar. In computer vision and computer graphics, it has been used to describe natural scenes, and to generate textures [29][24][30] 20] It is also well known that the scaling exponent, ff, of a fBm process provides the appearance of coarseness of a surface texture [29] Recent work in communication had argued convincingly that LAN traffic is more suitably to be modeled as a self similar process than as a conventional ....

B. Mandelbrot and H. Van Ness, "Fractional Brownian motions, fractional noises and applicatioins," in SIAM Review, vol. 10, Oct. 1968.

....is perceived as a future cause of networking congestion (6,7,18) This is because the LRD of self similar traffic has a heavy tailed distribution (6) which has drastic effects on the buffer occupancy. Practically, it means that providing more buffer space is not a solution to buffer saturation(23) Eventually the buffer will fill up. A natural question to ask would be: if CAC is conservative then why is it that cell loss still occurs The answer lies in the studies conducted at the end of the 1980 s and early 1990 s when it was first observed that packet traffic exhibited burstiness over ....

Mandelbrot B., and Van Ness J.W., 1968, "Fractional Brownian Motions, Fractional Noises and Applications" SIAM Review Vol. 10, No 4, 422-437.

....long range dependence persists in 1=f fi processes, the widely used ARMA model is not suitable in this case. Some of the models developed in the past are the superposition of Lorenzian spectra model [9] infinite continuous transmission line model [10] and fractional brownian motion model [11]. Waveletbased models have also been developed to analyze and synthesize approximate 1=f fi behavior [7] 8] under a new frequency domain 1=f fi process definition. All of the above models have provided insight into 1=f fi spectral behavior, there are still, however, difficulties involved ....

....x(t) is 1=f fi=2 . It should be noted that for fi 2, G(0) is not finite, which results in infinite variance in the underlying process. This will cause a problem when this linear filtering model is used in synthesizing 1=f fi data. The fractional brownian motion model bypasses this problem [11] by having finite variance. As a result, however, it can only approximate 1=f fi behavior. Since we are not going to use (4) in synthesizing 1=f fi processes, but rather in deriving the statistics of such a process, the model of (4) will serve our purpose. 3 Relationship Between 1=f fi ....

B. B. Mandelbrot and H. W. Van Ness, "Fractional Brownian Motions, Fractional Noises and Applications, " SIAM Rev. , Vol. 10, pp. 422-436, Oct. 1968.

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B. Mandelbrot and J. W. V. Ness, "Fractional Brownian motions, fractional noises and applications, " SIAM Review, vol. 10, pp. 422--437, Oct. 1968.

No context found.

B. B. Mandelbrot and J. W. V. Ness, "Fractional Brownian motion, fractional noises and applications," SIAM Reviews, vol. 10, pp. 422--437, 1968.

No context found.

B. B. Mandelbrot and J. W. van Ness, "Fractional Brownian Motions, Fractional Noises and Applications", SIAM Review, vol. 10, pp. 422--437, 1968.

No context found.

B. Mandelbrot and J. Ness, "Fractional brownian motions, fractional noises and applications," SIAM Review, vol. 10, pp. 422--437, 1968.

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B. Mandelbrot and J. Van Ness, "Fractional Brownian motion, fractional noises and applications", SIAM Rev., 1968.

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B. Mandelbrot and J. V. Ness, "Fractional brownian motion, fractional noises and applications," SIAM review, vol. 10, no. 4, pp. 422--437, 1968.

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B. B. Mandelbrot and J. W.Van Ness, "Fractional Brownian motions, fractional noises and applications," SIAM Rev., vol. 10, pp. 422--437, 1998.

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B. Mandelbrot and J. Van Ness, "Fractional brownian motion, fractional noises and applications," SIAM review, vol. 10, no. 4, pp. 422--437, 1968.

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B.B. Mandelbrot and J.W. van Ness (1968). "Fractional Brownian motions, fractional noises and applications," Siam Rev. 10, 422-437.

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B.B. Mandelbrot and J.W. van Ness (1968). "Fractional Brownian motions, fractional noises and applications," Siam Rev. 10, 422-437.

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