Statistics on crossings of discretized diffusions and local time (Q1180181)
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scientific article; zbMATH DE number 27211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Statistics on crossings of discretized diffusions and local time |
scientific article; zbMATH DE number 27211 |
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Statistics on crossings of discretized diffusions and local time (English)
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27 June 1992
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It is shown that under some technical assumptions the zero crossings (properly standardized) of a discretized diffusion process \(dX_ t=b(X_ t,\theta_ 0)dt+dW_ t\) converge to the local time of \(X\). As a second result it is proved that the MLE of \(\theta_ 0\) based on \(Z_ k^{(n)}=\hbox{sgn} X_{k/n}\), \(0\leq k<n\), is an asymptotically normal (consistent) estimator for the unknown parameter \(\theta_ 0\).
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discretized diffusion
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local time
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estimator
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