  The Robbins-Monro algorithm is a recursive, simulation-based stochastic
procedure to approximate the zeros of a function that can be written as an
expectation. It is known that under some technical assumptions, Gaussian limit
distributions approximate the stochastic performance of the algorithm. Here, we
are interested in strong approximations for Robbins-Monro procedures. The main
tool for getting them are local limit theorems, that is, studying the
convergence of the density of the algorithm. The analysis relies on a version
of parametrix techniques for Markov chains converging to diffusions. The main
difficulty that arises here is the fact that the drift is unbounded.
