论文标题
平滑转换的明确固定点
Explicit fixed points of the smoothing transformation
论文作者
论文摘要
我们处理等式$ y \ stackrel {\ rm d} {=} \ frac {1} {b} \ sum_ {1 \ le j \ le j \ le j \ le j \ le j \ le n} w_jy_j $，未知的是$ y $的分布，$ y y y y y y y是$ y_j $ y y_jj $，$ y_j $ n属于$ y_jj $ n n是$ y_jj $，随机变量和$ w_j $是等分分布的，无负和期望〜1。通常，将解决方案作为Martingale的极限。在某些情况下，我们为$ y $的法律提供明确的公式。
We deal with the equation $Y \stackrel{\rm d}{=} \frac{1}{b} \sum_{1\le j\le N} W_jY_j$, where the unknown is the distribution of $Y$, the variables in the right hand side are independent, the $Y_j$ are equidistributed with $Y$, $N$ is an integer valued random variable, and the $W_j$ are equidistributed, nonnegative and of expectation~1. Usually a solution is obtained as the limit of a martingale. In some cases we give an explicit formula for the law of $Y$.
