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In this paper we prove that under certain assumptions the transient randomwalk in random environment with bounded jumps (in $\mathbb{Z}$) grows muchslower than the speed $n$. Precisely, there is $0<s<1$, such that although$X_n\rto$ we have  $\frac{X_n}{n^{s'}}\rightarrow 0$ for $0<s<s'$ almost surely.

On the slowdown of random walk in random environment with bounded jumps