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Abstract
In this paper, through wavelet methods, we obtain the energy of convolution of two-dimension exponential random variables and analyze its some properties of wavelet alternation, and we obtain some new results.
Key words
Exponential random variables; Wavelet alternation; Convolution; Energy
1.INTRODUCTION
The stochastic system is very important in many aspects. With the rapid development of computerized scientific instruments comes a wide variety of interesting problems for data analysis and signal processing. Infields rangingfromExtragalacticAstronomyto MolecularSpectroscopyto Medical Imagingtocomputer vision, One must recover a signal, curve, image, spectrum, or density from incomplete, indirect, and noisy data .Wavelets have contributed to this already intensely developed and rapidly advancingfield.
Recently, some persons have studied wavelet problems of stochastic processes or stochastic system (see[1]-[17]).
2.BASIC DEFINITION
Definition 1Let xi,i = 1,......n, be independent exponential random variables with respective ratesλi,i = 1,......n, and suppose thatλi!λj, ( i!j), The random variablen
=
3.ENERGY
x(t)dt(6) Use (6), we have
w(s, x) =
REFERENCES
[1]Cambancs (1994). Wavelet Approximation of Deterministic and Random Signals. IEEE Tran. on Information Theory, 40(4), 1013-1029.
[2]Flandrin (1992). Wavelet Analysis and Synthesis of Fractional Brownian Motion. IEEE Tran. on Information Theory, 38(2), 910-916.
[3]Krim (1995). Multire Solution Analysis of a Class of Nonstationary Processes. IEEE Tran. on Information Theory, 41(4), 1010-1019
[4]Haobo Ren (2002). Wavelet Estimation for Jumps on a Heterosedastic Regression Model. Acta Mathematica Scientia, 22(2), 269-277.
[5]Xuewen Xia (2005). Wavelet Analysis of the Stochastic System with Coular Stationary Noise. Engineering Science, (3), 43-46.
[6]XuewenXia (2008).Wavelet DensityDegreeof ContinuousParameterAR Model.InternationalJournal Nonlinear Science, 7(4).
[7]Xuewen Xia & Kai Liu (2007). Wavelet Analysis of Browain Motion. World Journal of Modelling and Simulation, (3).
[8]I.Daubechies(1993).DifferentPerspectiveonWavelets. InProceedingsofSymposiainAppliedMathematics, Vol. 46, 1993.
[9]M. Rosenblatt (1974). Random Processes. New York: Springer.
[10] S. Mallat & W. Hwang (1992). Singularity Dectection and Processing with Wavelets. IEEE Trans. on Information Theory, 38, 617-643.
[11] J. Zhang & G. Walter (1994). A Wavelet Based K-L-like Expansion for Wide-Sense Stationary Process. IEEE Trans. Sig. Proc..
[12] XuewenXia&TingDai (2009).Wavelet DensityDegreeofaClass ofWienerProcesses.International Journal Nonlinear Science, 8(3).
[13] Y. Meyer (1990). Ondelettes et Operatears. Hermann.
[14] Xuewen Xia (2010). Haar Wavelet Density of the Linear Regress Processes with Rondom Coefficient. In Proceedings of the Third International Conference on Modeling and Simulation, 2010(5).
[15] Xuewen Xia (2010).The Haar Wavelet Density of the Two Order Polynomial Stochastic Processes. In Proceedings of the Third International Conference on Modeling and Simulation, 2010(3).
[16] Xuewen Xia (2011). The Study of Wiener Processes with N(0,1)-Random Trend Peocesses Based on Wavelet. Journal Information and Computing Science, (2).
[17] Xuewen Xia (2011).The Study of a Class of the Fractional Brownian Motion Based on Wavelet. Inter. J. of Nonlinear Science, (3).
In this paper, through wavelet methods, we obtain the energy of convolution of two-dimension exponential random variables and analyze its some properties of wavelet alternation, and we obtain some new results.
Key words
Exponential random variables; Wavelet alternation; Convolution; Energy
1.INTRODUCTION
The stochastic system is very important in many aspects. With the rapid development of computerized scientific instruments comes a wide variety of interesting problems for data analysis and signal processing. Infields rangingfromExtragalacticAstronomyto MolecularSpectroscopyto Medical Imagingtocomputer vision, One must recover a signal, curve, image, spectrum, or density from incomplete, indirect, and noisy data .Wavelets have contributed to this already intensely developed and rapidly advancingfield.
Recently, some persons have studied wavelet problems of stochastic processes or stochastic system (see[1]-[17]).
2.BASIC DEFINITION
Definition 1Let xi,i = 1,......n, be independent exponential random variables with respective ratesλi,i = 1,......n, and suppose thatλi!λj, ( i!j), The random variablen
=
3.ENERGY
x(t)dt(6) Use (6), we have
w(s, x) =
REFERENCES
[1]Cambancs (1994). Wavelet Approximation of Deterministic and Random Signals. IEEE Tran. on Information Theory, 40(4), 1013-1029.
[2]Flandrin (1992). Wavelet Analysis and Synthesis of Fractional Brownian Motion. IEEE Tran. on Information Theory, 38(2), 910-916.
[3]Krim (1995). Multire Solution Analysis of a Class of Nonstationary Processes. IEEE Tran. on Information Theory, 41(4), 1010-1019
[4]Haobo Ren (2002). Wavelet Estimation for Jumps on a Heterosedastic Regression Model. Acta Mathematica Scientia, 22(2), 269-277.
[5]Xuewen Xia (2005). Wavelet Analysis of the Stochastic System with Coular Stationary Noise. Engineering Science, (3), 43-46.
[6]XuewenXia (2008).Wavelet DensityDegreeof ContinuousParameterAR Model.InternationalJournal Nonlinear Science, 7(4).
[7]Xuewen Xia & Kai Liu (2007). Wavelet Analysis of Browain Motion. World Journal of Modelling and Simulation, (3).
[8]I.Daubechies(1993).DifferentPerspectiveonWavelets. InProceedingsofSymposiainAppliedMathematics, Vol. 46, 1993.
[9]M. Rosenblatt (1974). Random Processes. New York: Springer.
[10] S. Mallat & W. Hwang (1992). Singularity Dectection and Processing with Wavelets. IEEE Trans. on Information Theory, 38, 617-643.
[11] J. Zhang & G. Walter (1994). A Wavelet Based K-L-like Expansion for Wide-Sense Stationary Process. IEEE Trans. Sig. Proc..
[12] XuewenXia&TingDai (2009).Wavelet DensityDegreeofaClass ofWienerProcesses.International Journal Nonlinear Science, 8(3).
[13] Y. Meyer (1990). Ondelettes et Operatears. Hermann.
[14] Xuewen Xia (2010). Haar Wavelet Density of the Linear Regress Processes with Rondom Coefficient. In Proceedings of the Third International Conference on Modeling and Simulation, 2010(5).
[15] Xuewen Xia (2010).The Haar Wavelet Density of the Two Order Polynomial Stochastic Processes. In Proceedings of the Third International Conference on Modeling and Simulation, 2010(3).
[16] Xuewen Xia (2011). The Study of Wiener Processes with N(0,1)-Random Trend Peocesses Based on Wavelet. Journal Information and Computing Science, (2).
[17] Xuewen Xia (2011).The Study of a Class of the Fractional Brownian Motion Based on Wavelet. Inter. J. of Nonlinear Science, (3).