WAVELET REPRESENTATIONS OF STOCHASTIC-PROCESSES AND MULTIRESOLUTION STOCHASTIC-MODELS

Deterministic signal analysis in a multiresolution framework through t he use of wavelets has been extensively studied very successfully in r ecent years. In the context of stochastic processes, the use of wavele t bases has not yet been fully investigated. In this paper, we use com pactly supported wavelets to obtain multiresolution representations of stochastic processes with paths in L2 defined in the time domain. We derive the correlation structure of the discrete wavelet coefficients of a stochastic process and give new results on how and when to obtain strong decay in correlation along time as well as across scales. We s tudy the relation between the wavelet representation of a stochastic p rocess and multiresolution stochastic models on trees proposed by Bass eville et al. We propose multiresolution stochastic models on the disc rete wavelet coefficients as approximations to the original time proce ss. These models are simple due to the strong decorrelation of the wav elet transform. Experiments show that these models significantly impro ve the approximation in comparison with the often used assumption that the wavelet coefficients are completely uncorrelated.