The generalized Ornstein-Uhlenbeck process is derived from a bivariate Lévy process and is suggested as a continuous time version of a stochastic recurrence equation . In this paper we consider the generalized Ornstein-Uhlenbeck process and provide sufficient conditions under which the process is exponentially ergodic and hence holds the expo-nentially β-mixing property. Our results can cover a wide variety of areas by selecting suitable Lévy processes and be used as fundamental tools for statistical analysis concerning the processes. Well known stochastic volatility models in finance such as Lévy-driven Ornstein-Uhlenbeck process is examined as a special case.
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