Estimation of quadratic variation for two-parameter diffusions

Details Estimation of quadratic variation for two-parameter diffusions Estimation of quadratic variation for two-parameter diffusions

2008-01-19

arxiv.org/abs/0801.3027v1

Mathematics

Probability

29 pages

Scientific paper

In this paper we give a central limit theorem for the weighted quadratic variations process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations $\sum_{i=1}^{[n s]} \sum_{j=1}^{[n t]} | \Delta_{i,j} Y |^2$ of a two-parameter diffusion $Y=(Y_{(s,t)})_{(s,t)\in[0,1]^2}$ observed on a regular grid $G_n$ is an asymptotically normal estimator of the quadratic variation of $Y$ as $n$ goes to infinity.

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