Jaka Sembiring

Diffusive representation of N-th order fractional brownian motion

Abstract This paper describes an effort to give a different representation of a newly Introduced n-th order fractional Brownian motion (n-fBm). The new representation is called diffusive representation which has been successfully applied to the 1/f α fractional noise. Thus this paper generalizes such representation to cover also n-fBm which is an extension to the ordinary fBm, due to the fact that the spectral properties of n-fBm cover larger range of parameter α. Different from 1/f α case, the solution involves finite part concept of theory of distribution. The advantage of the proposed method on synthesizing sample of n-fBm is presented.

Application of Multiple Tree Stochastic Theory on Estimating Signal over Network

Abstract A new multi-scale stochastic theory called the Multiple Tree (MT) theory, will be presented in this paper. The MT construction is a concatenate of several single trees where these trees are connected each other through a Gaussian random vector. As a family of multi-scale stochastic system, the MT is also closely related to the fractal phenomena. The nature of the MT is suitable to the computer network environment. In this paper such advantage will be exploited in estimating 1/f signal given ill-posed observation over the network.

Parameter Estimation of Fractional Brownian Motion Processes: Wavelet Packets Based

Abstract Correlation structure of wavelet packets will be derived first. Then it will be proved that for fractional Brownian motion (fBm) processes, correlation coefficients will decrease exponentially across the wavelet packets scales-in other words almost KL-expansion. Based on the derived theorem, it is possible to estimate the parameters of fBm processes. Flexibility of the wavelet packet structure permits us to choose the bases accordingly. From simulation results it can be concluded that by utilizing wavelet packets it is possible to get better estimate with fewer computation than the previously announced wavelet based estimation method.

STOCHASTIC PROCESS ON MULTIWAVELET

Abstract This paper describes a multi-scale stochastic model defined on a multiwavelet structure. Previously such stochastic models are based either on a single or multiple binary tree as well as on an ordinary wavelet structure. The proposed model lies on a tree structure consists of several sets of data coefficients as a result of multiwavelet transformation. Each data sets is linked only through initial data set at root node and conditionally independent given this initial state. Multiwavelet possesses several interesting properties like simultaneously short support, symmetry and orthogonality. The effect of these properties on the proposed model is shown through simulation of smoothing process of a certain fractal signal. It will be demonstrated that several improvements over previously announced results are obtained.