Title :
The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA
fDate :
1/1/1993 12:00:00 AM
Abstract :
The wavelet transform of random processes with wide-sense stationary increments is shown to be a wide-sense stationary process whose correlation function and spectral distribution are determined. The second-order properties of the coefficients in the wavelet orthonormal series expansion of such processes is obtained. Applications to the spectral analysis and to the synthesis of fractional Brownian motion are given
Keywords :
Brownian motion; spectral analysis; stochastic processes; wavelet transforms; correlation function; fractional Brownian motion; orthonormal series expansion; random processes; spectral analysis; spectral distribution; stochastic processes; wavelet transform; wide-sense stationary increments; Brownian motion; Continuous wavelet transforms; Fourier transforms; Random processes; Signal processing; Signal synthesis; Spectral analysis; Stochastic processes; Wavelet analysis; Wavelet transforms;
Journal_Title :
Information Theory, IEEE Transactions on
