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GENERALIZED FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES | ||
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An extended version of the fractional Ornstein-Uhlenbeck (FOU) process of which integrand is replaced by the exponential function of an independent L\'evy process is considered.@We call the process the generalized fractional Ornstein-Uhlenbeck (GFOU) process. The process is also constructed by replacing the variable of integration of the generalized Ornstein-Uhlenbeck process (GOU) with an independent fractional Brownian motion (FBM). The stationary property and the auto-covariance function of the process are studied. Consequently, some conditions of stationarity and the long memory property of the process are obtained.@Note that GFOU has both jumps and the long memory property, following the stream of extensions of ordinary Ornstein-Uhlenbeck process. | ||