论文标题
线性随机字段的局部限制定理
A Local Limit Theorem for Linear Random Fields
论文作者
论文摘要
在本文中，我们建立了一个局部限制定理，用于由自变量和相同分布的创新构建的随机变量的线性场，每次都有有限的第二刻。当绝对可以总结系数时，我们不会限制总结区域。但是，当系数仅是正方形的时，我们会在矩形工会上添加变量，并且根据所考虑的矩形数量，我们对系数施加规律性条件。我们的结果对于维度1也是新的，即对于随机变量的线性序列。这些示例包括仿真研究结果的分数集成过程。
In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do not restrict the region of summation. However, when the coefficients are only square-summable we add the variables on unions of rectangle and we impose regularity conditions on the coefficients depending on the number of rectangles considered. Our results are new also for the dimension 1, i.e. for linear sequences of random variables. The examples include the fractionally integrated processes for which the results of a simulation study is also included.
