Parameter Estimation of Complex Fractional Ornstein-Uhlenbeck Processes with Fractional Noise

Abstract

We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart, [Statist. Probab. Lett., 80 (2010), 1030-1038] to a special 2-dimensions. The strategy is to exploit the Garsia-Rodemich-Rumsey inequality and complex fourth moment theorems. The main ingredients of this paper are the sample path regularity of a multiple Wiener-Ito integral and two equivalent conditions of complex fourth moment theorems in terms of the contractions of integral kernels and complex Malliavin derivatives.

arXiv comment16 pages

References in corpus (2)

• Fourth Moment Theorems for complex Gaussian approximation
• Product Formula, Independence and Asymptotic Moment-Independence for Complex Multiple Wiener-Ito Integrals

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• A note on the Moment of Complex Wiener-Ito Integrals