论文标题
与独立随机变量的加权总和的大量法律：质量游戏
Laws of large numbers for weighted sums of independent random variables: a game of mass
论文作者
论文摘要
我们考虑由增量序列调节的独立随机变量的加权总和。我们提供操作条件，以确保大量规律，以便在中心和非中心案件中持有此类款项。强大定律的现有标准是隐式或假设系数序列的足够衰变。在我们的设置中，我们允许任意系数序列，可能是随机的，前提是通过这种增量调节的随机变量满足某些轻度浓度条件。在非中心情况下，可以将收敛转化为确定性序列的行为，并且只要随机变量的期望是增量的函数，它就会成为质量游戏。我们展示了如何通过识别几类增量来出现不同的限制方案，以提供具体的示例。
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The existing criteria for the strong law are either implicit or assume some sufficient decay for the sequence of coefficients. In our set up we allow for arbitrary sequence of coefficients, possibly random, provided the random variables regulated by such increments satisfy some mild concentration conditions. In the non-centered case, convergence can be translated into the behavior of a deterministic sequence and it becomes a game of mass provided the expectation of the random variables is a function of the increments. We show how different limiting scenarios can emerge by identifying several classes of increments, for which concrete examples will be offered.
