Second-order statistics of the wavelet transform of multiplicative white stochastic process

We determine the second-order statistics of the wavelet transform of a class of non-stationary random process which may be interpreted as a deterministic signal being corrupted by a multiplicative white stochastic process. The correlation function of the wavelet transform of the process is obtained in terms of wavelet ambiguity function (in Woodward´s (1953) sense). The upper-bound of the variance of the wavelet transform of the process is given. We show that for a narrow-band signal the upper-bound has an asymptotic decay of (2a)^-α, where a and α represent, respectively, the scale level of the wavelet transform of the process and the wavelet regularity parameter. Applications of the result are discussed