Estimation of quadratic variation for two-parameter diffusions

Abstract

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 ${\sum }_{i=1}^{[ns]}{\sum }_{j=1}^{[nt]}|{\Delta }_{i,j}Y{|}^2$ 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.

29 pages

References in corpus (3)

• Central limit theorems for sequences of multiple stochastic integrals
• Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
• Weighted power variations of iterated Brownian motion