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A stochastic process is a collection of random variables usually indexed by a totally ordered set.
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Nonparametric estimation in diffusion
Based on high frequency data, it is not possible to estimate the process $\left(\sigma_{t}\right)_{t\geq 0}$. More precisely, there is no way to estimate the sign of it. Note that, if $W_{t}$ is a sta …
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Subclass of semimartingales for which all characteristics can be estimated?
Since Iam not allowed to post comments, I have to post it as an answer:
You may consult Ito or not? by Jean Jacod and Ait Sahalia.
There are at least partial answers to your questions.