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This paper presents a new model, the HMM/Mix-SDTG, which describes Markov processes under control of a global vector variable called style variable. We present an EM learning algorithm to learn an HMM/Mix-SDTG from one or more 3D motion capture sequences labelled by their style values. Because each dimension of the style variable has explicit physical meaning, with the presented synthesis algorithm, we are able to generate arbitrarily new motion with style exactly as demand by specifying a style value. The output densities of HMM/Mix-SDTG is represented by mixtures of stylized decomposable triangulated graphs (Mix-SDTG), which, in addition to parameterizing the Markov process with the style variable, also achieve more numerical robustness and preventing common artifacts of 3D motion synthesis.