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With the help of a general methodology of asymptotic expansions for mixing processes, we obtain an asymptotic expansion for a special class of stochastic processes which is partly described by a stati...onary non-Gaussian Ornstein-Uhlenbeck process (OU process) with an invariant distribution $ F $. Our results include (i) a higher order asymptotics as well as a central limit theorem in Barndorff-Nielsen and Shephard’s stochastic volatility model; and also (ii) an asymptotic expansion for a natural estimator for the location of $ F $. The Malliavin calculus formulated by Bichteler, Gravereaux and Jacod for processes with jumps and the exponential mixing property of the OU process play substantial roles, where especially the former ensures a “conditional type Cramer condition” under a truncation. Owing to several inherent properties of OU processes, the regularity conditions for the expansions can be easily verified, and moreover, the coefficients of the expansions up to any order can be explicitly computed.show more
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2005-8