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

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...

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

We show that non orthogonal wavelets can characterize the frac tional Brownian motion fBm that is in white noise We demonstrate the point that discriminating the parameter of a fBm from that of noise is equivalent to discriminating the composite singularity formed by superimposing a peak singularity upon a Dirac singularity We characterize the composite singularity by formalizing this problem a...

A wavelet method for stochastic Volterra integral equations and its application to general stock model

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

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.