Abstract
This paper addresses the problem of estimating the drift parameter of the Ornstein– Uhlenbeck-type process driven by the sum of independent standard and fractional Brownian motions. With the help of some recent results on the canonical representation and spectral structure of mixed processes, the maximum likelihood estimator is shown to be consistent and asymptotically normal in the large-sample limit.
| Original language | English |
|---|---|
| Pages (from-to) | 408-425 |
| Number of pages | 18 |
| Journal | Theory of Probability and its Applications |
| Volume | 63 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019 Society for Industrial and Applied Mathematics.
Keywords
- Fractional Brownian motion
- Maximum likelihood estimator
- Ornstein
- Singularly perturbed integral equation
- Uhlenbeck process
- Weakly singular integral operator
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