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Berry–Esseen–Stein–Malliavin Theory for Fractional Ornstein–Uhlenbeck Process

In: Parameter Estimation in Stochastic Volatility Models

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  • Jaya P. N. Bishwal

    (University of North Carolina at Charlotte, Department of Mathematics and Statistics)

Abstract

Using Malliavin calculus along with Stein’s equation, the chapter shows that the distribution of the normalized minimum contrast estimator of the drift parameter in the fractional Ornstein–Uhlenbeck process observed over [0, T] converges to the standard normal distribution with a uniform error rate of the order O(T −1∕2) for the case H > 1∕2 where H is the Hurst exponent of the fractional Brownian motion driving the Ornstein–Uhlenbeck process. Then based on discrete observations, it introduces several approximate minimum contrast estimators and studies their rate of weak convergence to normal distribution.

Suggested Citation

  • Jaya P. N. Bishwal, 2022. "Berry–Esseen–Stein–Malliavin Theory for Fractional Ornstein–Uhlenbeck Process," Springer Books, in: Parameter Estimation in Stochastic Volatility Models, chapter 0, pages 411-487, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-03861-7_13
    DOI: 10.1007/978-3-031-03861-7_13
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