一类格子上有限维不可约随机游动常返性的证明

摘要

lattice random walk on random process theory is considered a special class of random walk. The recurrence and the non-recurrence are one of the important property of random walks. The recurrence problem of lattice random walk on random is studied in the paper. It is proved that m≥S dimensional lattice random walk on random,which is different from the one-dimensional (Eζ1 =0) or two-dimensional irreducibility,is non-recurrence. The conclusion solves the recurrence problem of some random walks.%格子上的随机游动是随机过程理论中的一类比较特殊的随机游动.而常返性和非常返性则是这一类随机游动所讨论的一条重要性质，对于一维格子上(Eξ1=0)的随机游动是常返的，对于二维格子上的不可约随机游动也是常返的，而对于维数大于或等于3的情形和一维和二维的并不一样，文章主要证明了其是非常返的.这个结论又解决了一类随机游动的一个常返性问题.