Fractional Brownian Motion and Sheet as White Noise Functionals

In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.

Anisotropic Fractional Brownian Random Fields as White Noise Functionals

This investigation aims at a new construction of anisotropic fractional Brownian random fields by the white noise approach. Moreover, we investigate its distribution and sample properties （stationariness of increments, self-similarity, sample continuity） which will furnish some useful views to future applications.

Temporal variation of noise correlation function(NCF) in Beijing and surroundings:Its relation with climate events and implications

Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to characterize the quality of NCF at each station pair. The SNR （in dB） is shown to be dependent on the separation distance R of the station pair via SNR= A -BlogR. ＇Normalized average SNR＇ for all the station pairs can then be calculated, as represented by the value of SNR taking R = 250 km in the empirical SNR-R relation, to measure the overall quality of the NCF result. The ＇normalized average SNR＇ of the NCF shows temporal variation and is apparently dependent on the root-mean-square （RMS） velocity of the microseism. The result obtained by this experiment provides clues to the explanation of the properties of NCF, such as the dominant mechanism underlying （diffuse wave fields or uncorrelated sources）, and the dependence of SNR on the time length of recordings.

The influences of large earthquake signals on the recovery of surface waves from ambient noise cross-correlation functions

Ambient noise tomography(ANT)has been widely used to image crust and upmost mantle structures.ANT assumes that sources of ambient noise are diffuse and evenly distributed in space and the energy of different modes is equipartitioned.At present,the sources of the primary and the secondary microseisms are well studied,but there are only a few on the studies of long-period ambient noise sources.In this study,we study the effects of large earthquake signals on the recovery of surface waves from seismic ambient noise data recorded by seismic stations from the US permanent networks and Global Seismographic Network(GSN).Our results show that large earthquake signals play an important role on the recovery of long-period surface waves from ambient noise cross-correlation functions.Our results are consistent with previous studies that suggest the contribution of earthquake signals to the recovery of surface waves from cross-correlations of ambient noise is dominant at periods larger than 20–40 s.

Research on Real-time Monitoring of Abnormal Seismic Noise

The noise data in vertical component records of 85 seismic stations in Fujian Province during 2012 is used as the research object in this paper. The noise data is divided into fiveminute segments to calculate the power spectra. The high reference line and low reference line of station are then identified by drawing a probability density function graph( PDF)using the power spectral probability density function. Moreover, according to the anomalies of PDF graphs in 85 seismic stations,the abnormal noise is divided into four categories: dropped packet, low noise, high noise, and median noise anomalies.Afterwards,four selection methods are found by the high or low noise reference line of the stations,and the system of real-time monitoring of seismic noise is formed by combining the four selection methods. Noise records of 85 seismic stations in Fujian Province in July2013 are selected for verification,and the results show that the anomalous noise-recognition system could reach a 90% success rate at most stations and the effect of selection are very good. Therefore,it could be applied to the seismic noise real-time monitoring in stations.

ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES

In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion

Novel copyright protection scheme for digital content

A novel copyright protection scheme for digital content is presented, which is a private watermarking scheme based on the watermark embedding in the DCT domain and watermark extraction Using independent component analysis （ICA）. The system includes the key for watermark extraction and the host image. The algorithm splits the original image into blocks and classifies these blocks based on visual masking, that is, noise visibility function （NVF）. Watermark components with different strength are inserted into chosen direct current components of DCT coefficients according to the classifier. The watermark extraction is based on the characteristic of the statistic independence of the host image, watermark and key. Principle component analysis （PCA） whitening process and FastICA techniques are introduced to ensure a blind watermark extraction without requiring the original image. Experirnental results show the proposed technique is robust under attacks such as image filtering and adding noise, cropping and resizing. In addition, the proposed private watermarking system can be improved to the application of the DTV content protection system.

Novel Design for High Speed and Resolution Delta-sigma A/D Converter

The delta-sigma converter is one of the high speed and resolution analog-to-digital modulators. Its implementation needs the low oversampling technique and the multi-bit D/A converter. The noise induced by the multi-bit D/A converter becomes one of the key factors deteriorating the signal-to-noise rate of the delta-sigma A/D converter. A novel structure with signal unity transfunction, dynamic element matching(DEM) and noise-shaping is discussed. The method is investigated to design converter based on the proposed structure. The behavior simulation indicates that the structure and the design method are feasible.

Least squares weighted twin support vector machines with local information

A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information(LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.

STABILITY OF SOME KIND OF STOCHASTIC DIFFERENTIAL EQUATION

In this paper,a kind of stochastic differential equation is investigated and the almost sure exponential stability of the equation is obtained using Gronwall’s inequality.Further,we also give other noise intensity function to keep the stability of the system.