Download e-book for iPad: An Introduction to Econophysics: Correlations and Complexity by Rosario N. Mantegna

By Rosario N. Mantegna

ISBN-10: 0521620082

ISBN-13: 9780521620086

Statistical physics recommendations equivalent to stochastic dynamics, brief- and long-range correlations, self-similarity and scaling, let an realizing of the worldwide habit of monetary structures with no first having to determine a close microscopic description of the method. This pioneering textual content explores using those strategies within the description of economic structures, the dynamic new strong point of econophysics. The authors illustrate the scaling options utilized in chance idea, severe phenomena, and fully-developed turbulent fluids and follow them to monetary time sequence. additionally they current a brand new stochastic version that screens numerous of the statistical houses saw in empirical facts. Physicists will locate the appliance of statistical physics strategies to fiscal structures interesting. Economists and different monetary execs will enjoy the book's empirical research equipment and well-formulated theoretical instruments that may let them describe platforms composed of an incredible variety of interacting subsystems.

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Extra resources for An Introduction to Econophysics: Correlations and Complexity in Finance

Example text

13) n 18 Random walk Fig. 3. Top: Simulation of P (Sn ) for n ranging from n = 1 to n = 250 for the case when P (x) is a double triangular function (inset). Bottom: Same distribution using scaled units. and P˜ (˜ x) ≡ P (˜ x)n1/2 . 14) By analyzing the scaled pdfs P˜ (˜ x) observed at large values of n in Figs. 4, we note that the distributions rapidly converge to the functional form of the Gaussian of unit variance (shown as a smooth curve for large n). We emphasize the fundamental hypothesis of the CLT.

3 Central limit theorem Suppose that a random variable Sn is composed of many parts xi , Sn = n i=1 xi , such that each xi is independent and with finite variance E{xi } = 0, E{x2i } = s2i , and n σn2 = E{Sn2 } = s2i . 10) i=1 where, for every > 0, Ui is a truncated random variable that is equal to xi when |xi | ≤ σn and zero otherwise. 12) PG (S˜n ) = √ exp(−S˜n2 /2). 2π A formal proof of the CLT is given in probability texts such as Feller [56]. Using two concrete examples, we ‘illustrate’ the main point of the theorem, the gradual convergence of P (Sn ) to the Gaussian shape when n increases.

Let 50 Stationarity and time correlation us consider a stochastic process with a power spectrum of the form S(f) = const. 21) with 0 < η < 2. In the last section we saw that the case η = 0 corresponds to white noise, while η = 2 corresponds to the Wiener process. When η ≈ 1, a stochastic process characterized by a spectral density as in Eq. 21) is called 1/f noise, while the general case 0 < η < 2 is sometimes called 1/f η noise. 1/f noise has been observed in a wide variety of phenomena, ranging from the current fluctuations in diodes and transistors to the fluctuations in traffic flow on a highway [46, 79, 103, 136, 156].

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An Introduction to Econophysics: Correlations and Complexity in Finance by Rosario N. Mantegna


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