一类随机线性方程组的一个极限性质

A Limiting Property On A Kind Of Large System Of Random Linear Equations

考虑了一类形如X_n=V_n+n^(-r)W_nX_n 的随机线性方程组解的极限性质问题,其中W_n 是n 阶随机矩阵,它的元为独立同分布随机变量,X_n 和V_n 为n 维列向量。证明了若系数随机矩阵元的1+p 阶矩存在,则当n 趋于无穷时,随机线性方程组的解是强相合的。

There is presented some limit property for the solution of a kind of ra- ndom linear equations,which have the form X_(?)=V_(?)+n^(-(?))W_(?)X_(?),where W_(?) are n×n random matrices with i.i.d.entries and X_(?) and V_(?) are n-dimensional column vectors,It is proved that the solutions of these random linear equations are strongly consistent as n tends to infinite if the 1+p order moment of each (?)ntry is finite.