  We study the convergence rate of randomly truncated stochastic algorithms,
which consist in the truncation of the standard Robbins-Monro procedure on an
increasing sequence of compact sets. Such a truncation is often required in
practice to ensure convergence when standard algorithms fail because the
expected-value function grows too fast. In this work, we give a self contained
proof of a central limit theorem for this algorithm under local assumptions on
the expected-value function, which are fairly easy to check in practice.
