  We obtain non asymptotic concentration bounds for two kinds of stochastic
approximations. We first consider the deviations between the expectation of a
given function of the Euler scheme of some diffusion process at a fixed
deterministic time and its empirical mean obtained by the Monte-Carlo
procedure. We then give some estimates concerning the deviation between the
value at a given time-step of a stochastic approximation algorithm and its
target. Under suitable assumptions both concentration bounds turn out to be
Gaussian. The key tool consists in exploiting accurately the concentration
properties of the increments of the schemes. For the first case, as opposed to
the previous work of Lemaire and Menozzi (EJP, 2010), we do not have any
systematic bias in our estimates. Also, no specific non-degeneracy conditions
are assumed.
