论文标题
Martingale序列的连续性模量
Modulus of continuity for a martingale sequence
论文作者
论文摘要
给定满足界限自然假设的随机场的序列序列，这表明该序列的刻度极限可以通过保留一定类别的连续性模量的方式进行修改。也就是说，如果序列的每个元素都接受了给定的连续性模量，则可以构造限制随机场的修改，以便该新场也可以接受相同的连续性模量。此外，可以证明，需要进一步的平滑度和对原始序列的界限更强的概念确保了限制场的进一步平滑度，并且更强大的收敛方式到此极限。此外，还为衍生物保留了连续性模量。
Given a martingale sequence of random fields that satisfies a natural assumption of boundedness, it is shown that the pointwise limit of this sequence can be modified in such a way that a certain class of moduli of continuity is preserved. That is, if every element of the sequence admits a given modulus of continuity, one can construct a modification of the limiting random field so that this new field also admits the same modulus of continuity. Additionally, it is shown that requiring further smoothness and a stronger notion of boundedness for the original sequence guarantees further smoothness of the limiting field and a stronger mode of convergence to this limit. Moreover, the modulus of continuity is also preserved for the derivatives.
