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 dir...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.展开更多
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 increment...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.展开更多
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 charact...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.展开更多
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 ...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.展开更多
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 ...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展开更多
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 anal...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.展开更多
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 fu...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.展开更多
文摘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.
基金Supported by the National Natural Science Foundation of China (No.10171035)
文摘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.
基金supported by the Fundamental Research and Development of Institute of Geophysics,China Earthquake Administration (DQJB07B03)
文摘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.
基金supported by the National Natural Science Foundation of China(No.41874058).
文摘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.
基金supported by the National Natural Science Fundation of China(71561017)the Science and Technology Plan of Gansu Province(1606RJZA041)+1 种基金the Youth Plan of Academic Talent of Lanzhou University of Finance and Economicssupported by the Fundamental Research Funds for the Central Universities(HUST2015QT005)
文摘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
基金This project was supported by the Digital TV Special Foundation of National Development and Reform Commission ofChina (040313) Home Coming Scholars Science Activity Foundation of Ministry of Personnel (20041231) the Graduate In-novation Foundation of Xidian University (innovaion 0509)
文摘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.
基金Supported by the Natural Science Foundation of Fujian Province (No.2010J01005)Scienceand Technology Development Foundation of Fuzhou University (No.2010-XQ-24)
文摘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.