  In this article subordination of random walks in $R^d$ is considered. We
prove that subordination of random walks in the sense of [BSC12] yields the
same process as subordination of L\'evy processes (in the sense of Bochner).
Furthermore, we prove that appropriately scaled subordinate random walk
converges to a multiple of a rotationally $2\alpha$-stable process if and only
if the Laplace exponent of the corresponding subordinator varies regularly at
zero with index $\alpha\in (0,1]$.
