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A class of continuous-time models is developed for modelling data with heavy tails and long-range dependence. These models are based on the Green function solutions of fractional differential equations driven by Lévy noise. Some exact results on the second- and higher-order characteristics of the equations are obtained. Applications to stochastic volatility of asset prices and macroeconomics are provided.
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Anh et al. (2002) studied this question.
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