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利用新方法证明了Zd上的瞬时α-稳定随机游动的值域几乎处处是一个离散Hausdorff维数为α的分形.虽然类似的结论对Zd上的严格α-稳定随机游动也成立,但是其证明方法对Zd上的瞬时α-稳定随机游动是完全不适用的.“,”In this paper we prove with a new method that the range of a transient α-stable random walk in Zd is a.s. a fractal of index α of discrete Hausdroff dimension. Though the analogous result holds for a strictly α-stable random walk in Zd, the proved method is not suitable for a transient α-stable random walk in Zd.