By R. J. Bhansali, P. S. Kokoszka (auth.), Prof. Govindan Rangarajan, Prof. Mingzhou Ding (eds.)
ISBN-10: 3540401296
ISBN-13: 9783540401292
ISBN-10: 3540448322
ISBN-13: 9783540448327
Processes with lengthy diversity correlations ensue in a wide selection of fields starting from physics and biology to economics and finance. This booklet, appropriate for either graduate scholars and experts, brings the reader modern in this quickly constructing box. A unique team of specialists were introduced jointly to supply a entire and well-balanced account of simple notions and up to date advancements. The booklet is split into components. the 1st half offers with theoretical advancements within the region. the second one half includes chapters dealing basically with 3 significant components of program: anomalous diffusion, economics and finance, and biology (especially neuroscience).
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Additional info for Processes with Long-Range Correlations: Theory and Applications
Example text
Sample path of a self-similar process. Starting with the sample path of a selfsimilar process, if one performs a dilation of the time axis of factor 1/c and a dilation on the amplitude axis of factor cH , one obtains a new sample path that is (statistically) indistinguishable from the original one. whose exponents are all controlled by the self-similarity parameter H. Besides the connection between scaling and power law, those relations also show that self-similar processes are non stationary ones.
G. Rangarajan, M. ): LNP 621, pp. 34–60, 2003. c Springer-Verlag Berlin Heidelberg 2003 Scaling and Wavelets: An Introductory Walk 35 market volatility or currency change rates fluctuations [29,51]. , high volatility in markets or large waiting times and congestions in computer network traffic or pathologies in body rythms. . ). The notion of scaling, however, remains defined poorly or in a loose way and may be related to a variety of different properties of a system or a process. A possible common tentative definition for scaling can be formulated through a negative statement: there is no characteristic scale (of time or space.
It is known that SAWs have asymptotic variance ∼ n6/(E+2) where E is the dimension of the Euclidean space for the random walk [11]. Although fBm is not a faithful model for SAW, these two models agree asymptotically if H = 3/(E +2). For E = 2 this corresponds to H = 34 . It will be interesting to find whether it is possible to use fBm as an approximated model for SAW. This entails defining a measure for the approximation and is intimately related to the mathematical concept of intersectional local time, in which the significance of H = 34 has been specifically noted [34].
Processes with Long-Range Correlations: Theory and Applications by R. J. Bhansali, P. S. Kokoszka (auth.), Prof. Govindan Rangarajan, Prof. Mingzhou Ding (eds.)
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