Recursive probability density estimation for weakly dependent stationary processes

Recursive estimation of the univariate probability density function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(x)</tex> for stationary processes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{Xⱼ\}</tex> is considered. Quadratic-mean convergence and asymptotic normality for density estimators <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fₙ(x)</tex> are established for strong mixing and for asymptotically uncorrelated processes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{Xⱼ\}</tex> . Recent results for nonrecursive density estimators are extended to the recursive case.