B. Mandelbrot, "A multifractal walk down wall street," Scientific American, pp. 70--73, Feb. 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....B(t) using the MRM M(t) The subordination of a Brownian process with a non decreasing process has been introduced by Mandelbrot and Taylor 11 [24] and is the subject of an extensive literature in mathematical finance. Multifractal subordinators have been considered by Mandelbrot and co workers [28] and widely used to build multifractal processes. Let us define the process X (t) as: Definition 9 (Subordinated MRW) Let B(t) a brownian motion (with E B(1) 1) and M(dt) a non degenerated MRM measure which is independent of B(t) The subordinated MRW process is the process defined ....

Mandelbrot B.B.: A Multifractal Walk Down Wall Street, Scientific American 280, 70-73 (1999).

....motion, Levy flights, # stable motion, wavelets, long range dependence, multifractal subordination. 1 Introduction and Summary Fractal processes have been instrumental in a variety of fields ranging from the theory of fully developed turbulence [73, 64, 36, 12, 7] to stock market modelling [28, 68, 69, 80], image processing [61, 21, 104] medical data [2, 98, 11] and geophysics [36, 65, 47, 92] In networking, models using fractional Brownian motion (fBm) have helped advance the field through their ability to assess the impact of fractal features such as statistical selfsimilarity and long range ....

.... 89, 88] Second, we carefully discuss basic examples as well as Brownian motion in multifractal time, B 1 2 (M(t) This process has recently been suggested as a model for stock market exchange by Mandelbrot who argues that oscillations in exchange rates occur in multifractal trading time [68, 69]. With the theory developed in this paper, it becomes an easy task to explore B 1 2 (M(t) from the multifractal point of view, and with # This property is also known as the Lvey modulus of continuity in the case of Brownian motion. For fBm see [5, Thm. 8.3.1. Introduction and Summary 3 0 1 2 3 ....

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B. Mandelbrot. A multifractal walk down wall street. Scientific American, 280(2):70--73, Feb. 1999.

.... indisputable component of empirical data observed in a wide variety of applications ranging from natural phenomena such as hydrodynamic turbulence [9] biology and body rhythms [27] to purely human phenomena created by mankind s activities such as computer networks [14, 20] and financial markets [15, 16]. Often, the presence of scaling in the data can be tied to crucial properties of the system, e.g. high volatility in markets and large waiting queues in computer networks. Being of major importance scaling phenomena call for both, appropriate tools of analysis with known accuracy as well as ....

B. B. Mandelbrot. A multifractal walk down wall street. Scientific American, 280(2):70--73, Feb. 1999.

.... and biology [1 3] In electrical engineering these processes have served as extremely useful models for characterizing textures in images [4 6] and noise in analog circuits [2] In finance, these processes have been recognized as important for characterizing price volatility and market risk [7, 8]. They have even impacted DNA research [9] Data networking conjures up many of the salient features of 1=f processes. Recently, traffic loads and interarrival times in data networks have been shown to exhibit LRD and self similar behavior [10] This behavior has proven to be a key factor driving ....

....are indeed authentic and not due to some artifact of the synthesis procedure. In addition to its potential applicability to networking, this research could also be useful for applications such as simulation of financial markets, where volatility is known to exhibit LRD and nonGaussian behavior [8, 45]. We are not limited to these few applications, however. The FFT algorithm could also be quite useful for benchmark testing of LRD parameter estimation algorithms. For instance, LRD processes with varying short term covariances and nonGaussian marginals could be synthesized to test the accuracy ....

B. Mandelbrot, "A multifractal walk down wall street," Scientific American, pp. 70--73, Feb. 1999.

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B. Mandelbrot, "A multifractal walk down wall street," Scientific American, pp. 70--73, Feb. 1999.

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