Estimation of fractional Brownian motion embedded in a noisy environment using nonorthogonal wavelets

Estimation of 2-D noisy fractional Brownian motion and its applications using wavelets

The two-dimensional (2-D) fractional Brownian motion (fBm) model is useful in describing natural scenes and textures. Most fractal estimation algorithms for 2-D isotropic fBm images are simple extensions of the one-dimensional (1-D) fBm estimation method. This method does not perform well when the image size is small (say, 32x32). We propose a new algorithm that estimates the fractal parameter ...

Estimation of D Noisy Fractional Brownian Motion and its Applications using Wavelets

The D fractional Brownian motion fBm model is useful in describing natural scenes and textures Most fractal estimation algorithms for D isotropic fBm images are simple extensions of the D fBm estimation method This method does not perform well when the image size is small say We propose a new algorithm that estimates the fractal parameter from the decay of the variance of the wavelet coe cients...

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

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