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Estimation of quadratic variation for two-parameter diffusions

被引：8
|
作者：
Reveillac, Anthony [1 ]
机构：
[1] Univ La Rochelle, Lab Math Image & Applicat, F-17042 La Rochelle, France
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2009年 / 119卷 / 05期
关键词：
Weighted quadratic variation process; Functional limit theorems; Two-parameter stochastic processes; Malliavin calculus; CONTINUOUS MARTINGALES; STOCHASTIC INTEGRALS; WEAK-CONVERGENCE; LIMIT-THEOREMS; FORMULA; MODELS;
D O I：
10.1016/j.spa.2008.08.006
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper we give a central limit theorem for the weighted quadratic variation process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations Sigma([ns])(i=1) Sigma([nt])(j=1) vertical bar Delta(i.j)Y vertical bar(2) of a two-parameter diffusion Y = (Y((s,t)))((s,t)is an element of[0,1]2) observed on a regular grid G(n) form an asymptotically normal estimator of the quadratic variation of Y as n goes to infinity. (C) 2008 Elsevier B.V.. All rights reserved.
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页码：1652 / 1672
页数：21
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