  In this paper, we mainly study the random sampling stability for signals in a
weighted reproducing kernel subspace of $L_\nu^p(\mathbb{R}^d)$ without the
additional requirement that the kernel function has symmetry. The sampling set
is independently and randomly drawn from a general probability distribution
over $\mathbb{R}^d$. Based on the frame characterization of weighted
reproducing kernel subspaces, we first approximate the weighted reproducing
kernel space by a finite dimensional subspace on any bounded domains. Then, we
prove that the random sampling stability holds with high probability for all
signals in weighted reproducing kernel subspaces whose energy concentrate on a
cube when the sampling size is large enough.
