  In this paper we prove large and moderate deviations principles for the
recursive kernel estimators of a probability density function defined by the
stochastic approximation algorithm introduced by Mokkadem et al. [2009. The
stochastic approximation method for the estimation of a probability density. J.
Statist. Plann. Inference 139, 2459-2478]. We show that the estimator
constructed using the stepsize which minimize the variance of the class of the
recursive estimators defined in Mokkadem et al. (2009) gives the same pointwise
LDP and MDP as the Rosenblatt kernel estimator. We provide results both for the
pointwise and the uniform deviations.
