Local and uniform moduli of continuity of chi-square processes

Let {eta(i)(t), t is an element of [0, 1]}(i=1)(k) be independent copies of eta = {eta(t), t is an element of [0, 1]}, a mean zero continuous Gaussian process. Let Y-k := Y-k(t) = Sigma(k)(i=1) eta(2)(i)(t), t is an element of [0, 1]. This paper shows how exact local (at 0) and uniform moduli of continuity (on [0,1]) of Y-k can be obtained from the exact local and uniform moduli of continuity of eta.