What question did this study set out to answer?

To characterize the wavelet transform of random processes with wide-sense stationary increments and demonstrate its application to the analysis and synthesis of fractional Brownian motion.

January 1, 1993IEEE Transactions on Information Theory

The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion

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Authors

EME. MasryNaval Information Warfare Center Pacific

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Implication

Theoretical analysis reveals stationary properties of wavelet-transformed increment processes, highlighting new frameworks for spectral analysis and fractional Brownian motion synthesis.

Key Points

To characterize the wavelet transform of random processes with wide-sense stationary increments and demonstrate its application to the analysis and synthesis of fractional Brownian motion.
Evaluated the mathematical properties of continuous and orthonormal wavelet transforms applied to random processes with wide-sense stationary increments.
Derived analytical expressions for the correlation functions and spectral distributions of the resulting transformed processes.
Calculated second-order statistical properties of the coefficients obtained from wavelet orthonormal series expansions.
Demonstrated that the wavelet transform of a process with wide-sense stationary increments yields a wide-sense stationary process.
Formulated the exact correlation function and spectral distribution for the wavelet coefficients across orthonormal series expansions.
Established theoretical frameworks directly enabling the spectral analysis and numerical synthesis of fractional Brownian motion.

Cite This Study

E. Masry (1993) studied this question.

synapsesocial.com/papers/6a9ae53be0750e5fb66badeb https://doi.org/10.1109/18.179371

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Implication

Theoretical analysis reveals stationary properties of wavelet-transformed increment processes, highlighting new frameworks for spectral analysis and fractional Brownian motion synthesis.

The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion

Discussion

Member takes

Implication

Key Points

Cite This Study

The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion

Discussion

Member takes

Implication

Key Points

Cite This Study

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