Recursive probability density estimation for weakly dependent stationary processes

Recursive estimation of the univariate probability density functionf(x)for stationary processes{X_{j}}is considered. Quadratic-mean convergence and asymptotic normality for density estimatorsf_{n}(x)are established for strong mixing and for asymptotically uncorrelated processes{X_{j}}. Recent results for nonrecursive density estimators are extended to the recursive case.