Let {X_{n}}_{n∈ℕ} be a sequence of i.i.d. random variables in ℤ^{d}. Let S_{k} = X_{1} + … + X_{k} and Y_{n}(t) be the continuous process on [0, 1] for which Y_{n}(k/n) = S_{k}/n^{1/2} for k = 1, … n and which is linearly interpolated elsewhere. The paper gives a generalization of results of ([2]) on the weak limit laws of Y_{n}(t) conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on ℤ^{d}: d ≧ 2 is the Brownian motion.
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