Limit theorems for power variations of ambit fields driven by white noise

被引：14
作者：
Pakkanen, Mikko S. [1 ,2 ]
机构：
[1] Aarhus Univ, CREATES, DK-8210 Aarhus V, Denmark
[2] Aarhus Univ, Dept Econ & Business, DK-8210 Aarhus V, Denmark
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2014年 / 124卷 / 05期
基金：
芬兰科学院; 新加坡国家研究基金会;
关键词：
Ambit field; Power variation; Law of large numbers; Central limit theorem; Chaos decomposition; LEVY-BAXTER THEOREM; STOCHASTIC-PROCESSES; QUADRATIC VARIATION; GAUSSIAN-PROCESSES; CONVERGENCE; SEMIMARTINGALES;
D O I：
10.1016/j.spa.2014.01.005
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：
We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power variations converge to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This result holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asymptotic behavior. Our second result is a stable central limit theorem for thinned power variations. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：1942 / 1973
页数：32
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