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Integral representations and properties of operator fractional Brownian motions
dichotomy principle integral representations long-range dependence multivariate Brownian motion operator fractional Brownian motion operator self-similarity
2011/3/18
Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar and (iii) stationary increment processes. They are the natural multivariate generalizations of the well-studie...
Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index
Horizontal visibility graphs transformed fractional Brownian motions Topological properties versus Hurst index
2010/12/28
Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes.In recent years, quite a few methods have been proposed to transform a single time series to a comp...
Extreme values of derivatives of smoothed fractional Brownian motions
Extreme values of derivatives smoothed fractional Brownian motions
2009/9/22
Let B,(.) be a fractional Brownian motion on R
with parameter 1/2 < H < 1, and consider its smoothed version
b;Hj K((t- sj/b,)BH(s) ds, teR, where the kernel K ( . ) is a density function
and the b...