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Summary form only given.The experimental realization of Bose-Einstein condensation has stimulated much interest in investigating the rich physics of these trapped weakly interacting Bose gases. Although much has been learned within the last several years, more subtle aspects of the condensation process and the quantum dynamics await further elucidation. In this paper, we use the well-established phase space techniques, in particular, the P-representation approach, to study the quantum dynamics of trapped degenerate Bose gases. The system under consideration is described by a Hamiltonian and a functional P-representation quasiprobability distribution is derived. We have developed a self-consistent approximation scheme, which allows us to solve the corresponding stochastic differential equations. Various results are reported.