Principal Component Analysis of Fractional Brownian Motion

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Wavelets for the Analysis, Estimation and Synthesis of Scaling Data

Long-range dependence-Scaling phenomena-(Multi)fractal-Wavelet analysis Scaling analysis-Scaling parameters estimation-Robustness-Fractional Brownian motion synthesis-Fano factor-Aggregation procedure-Allan variance.

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Karhunen–Loève expansion for multi-correlated stochastic processes

We propose two different approaches generalizing the Karhunen–Loève series expansion to model and simulate multi-correlated non-stationary stochastic processes. The first approach (muKL) is based on the spectral analysis of a suitable assembled stochastic process and yields series expansions in terms of an identical set of uncorrelated random variables. The second approach (mcKL) relies on expa...

Principal component analysis of 1 / f α noise

Principal component analysis (PCA) is a popular data analysis method. One of the motivations for using PCA in practice is to reduce the dimension of the original data by projecting the raw data onto a few dominant eigenvectors with large variance (energy). Due to the ubiquity of 1/f α noise in science and engineering, in this Letter we study the prototypical stochastic model for 1/f α processes...