Energy of the stochastic wave equation driven by a fractional Gaussian noise

2007 ◽  
Vol 15 (4) ◽  
pp. 303-326 ◽  
Author(s):  
Boris P. Belinskiy ◽  
Peter Caithamer
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Fractional Gaussian Noise ◽  
Stochastic Wave Equation

Energy of a string driven by a two-parameter Gaussian noise white in time

2001 ◽  
Vol 38 (04) ◽  
pp. 960-974 ◽  
Author(s):  
Boris P. Belinskiy ◽  
Peter Caithamer
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Spatial Dimension ◽  
Spatial Covariance ◽  
Stochastic Wave Equation ◽  
Two Parameter

In this paper we consider the stochastic wave equation in one spatial dimension driven by a two-parameter Gaussian noise which is white in time and has general spatial covariance. We give conditions on the spatial covariance of the driving noise sufficient for the string to have finite expected energy and calculate this energy as a function of time. We show that these same conditions on the spatial covariance of the driving noise are also sufficient to guarantee that the energy of the string has a version which is continuous almost surely.

Energy of a string driven by a two-parameter Gaussian noise white in time

2001 ◽  
Vol 38 (4) ◽  
pp. 960-974 ◽  
Author(s):  
Boris P. Belinskiy ◽  
Peter Caithamer
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Spatial Dimension ◽  
Spatial Covariance ◽  
Stochastic Wave Equation ◽  
Two Parameter

In this paper we consider the stochastic wave equation in one spatial dimension driven by a two-parameter Gaussian noise which is white in time and has general spatial covariance. We give conditions on the spatial covariance of the driving noise sufficient for the string to have finite expected energy and calculate this energy as a function of time. We show that these same conditions on the spatial covariance of the driving noise are also sufficient to guarantee that the energy of the string has a version which is continuous almost surely.

scholarly journals Fractional stochastic wave equation driven by a Gaussian noise rough in space

Bernoulli ◽  
2020 ◽  
Vol 26 (4) ◽  
pp. 2699-2726
Author(s):  
Jian Song ◽  
Xiaoming Song ◽  
Fangjun Xu
Keyword(s):  
Wave Equation ◽  
Gaussian Noise ◽  
Stochastic Wave Equation

scholarly journals Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

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