英文文献：Limit theorems for power variations of ambit fields driven by white noise-白噪声驱动范围场功率变化的极限定理
英文文献作者：Mikko S. Pakkanen
英文文献摘要：
We study the asymptotic behavior of lattice power variations of two-parameter ambit fields that are driven by white noise. Our first result is a law of large numbers for such power variations. Under a constraint on the memory of the ambit field, normalized power variations are shown to converge to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This law of large numbers holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asympotic behavior. Our second result is a related stable central limit theorem for thinned power variations. Additionally, we provide concrete examples of ambit fields that satisfy the assumptions of our limit theorems.

研究了白噪声驱动下双参数界场晶格功率变化的渐近性态。我们的第一个结果是这种幂次变化的大数定律。当晶格间距趋近于零时，正则化幂次变化收敛于与边界场相关的波动场的某些积分泛函。这个大数定律也适用于通过只包括由具有特定非对称行为的间隙分隔的增量来计算的减幂变化。我们的第二个结果是一个相关的减幂变化的稳定中心极限定理。此外，还给出了满足极限定理假设的范围场的具体例子。