论文标题
关于总和几乎肯定的收敛
On the almost sure convergence of sums
论文作者
论文摘要
提供了两个反描述，解决了在\ cite {ad}和\ cite {pz}中提出的问题。两个反例都与混沌有关。令$ f_n = y_n+z_n $。可能是$ f_n \ Overset {a.s。} \ longrightArrow 0 $，$ f_n \ Overset {l_ {2+δ}} \ longrightArrow 0 $和$ e \ e \ e \ bigl \ {\ sup_n \ { $ y_n $和$ z_n $属于统一的界限，但$ y_n $未能收敛到0 a.s。
Two counterexamples, addressing questions raised in \cite{AD} and \cite{PZ}, are provided. Both counterexamples are related to chaoses. Let $F_n=Y_n+Z_n$. It may be that $F_n\overset{a.s.}\longrightarrow 0$, $F_n\overset{L_{2+δ}}\longrightarrow 0$ and $E\bigl\{\sup_n\,\abs{F_n}^δ\bigr\}<\infty$, where $δ>0$ and $Y_n$ and $Z_n$ belong to chaoses of uniformly bounded degree, and yet $Y_n$ fails to converge to 0 a.s.
