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Gaussian and Hermite Ornstein-Uhlenbeck processes. (English) Zbl 1515.60184

Summary: In the present paper we study the asymptotic behavior of the auto-covariance function for Ornstein-Uhlenbeck (OU) processes driven by Gaussian noises with stationary and non-stationary increments and for Hermite OU processes. Our results are generalizations of the corresponding results of P. Cheridito et al. [Electron. J. Probab. 8, Paper No. 3, 14 p. (2003; Zbl 1065.60033)] and T. Kaarakka and P. Salminen [Commun. Stoch. Anal. 5, No. 1, 121–133 (2011; Zbl 1331.60065)].

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
60G10 Stationary stochastic processes
60G22 Fractional processes, including fractional Brownian motion
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