We provide an almost sure bound for oscillation rates of kernel density estimators for stationary processes, under the predictive dependence measures which are directly related to the data-generating mechanisms of the underlying processes. We also discuss moduli of continuity of the kernel density estimators.
"Oscillations and moduli of continuity of kernel density estimators under dependence." Rocky Mountain J. Math. 45 (5) 1659 - 1679, 2015. https://doi.org/10.1216/RMJ-2015-45-5-1659