Estimation of quadratic variation for two-parameter diffusions
Réveillac, Anthony
Original · EN
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 ∑ᵢ₌₁[ⁿ ˢ] ∑ⱼ₌₁[ⁿ ᵗ] | Δᵢ,ⱼ Y |² of a two-parameter diffusion Y=(Y₍ₛ,ₜ₎)₍ₛ,ₜ₎∈[₀,₁]₂ observed on a regular grid Gₙ is an asymptotically normal estimator of the quadratic variation of Y as n goes to infinity.
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