Local and uniform moduli of continuity of chi–square processes

Abstract

Let {ηi(t),t∈[0,1]}i=1k be independent copies of η={η(t),t∈[0,1]}, a mean zero continuous Gaussian process. Let Yk:=Yk(t)= ∑i=1kηi2(t),t∈[0,1]. This paper shows how exact local (at 0) and uniform moduli of continuity (on [0,1]) of Yk can be obtained from the exact local and uniform moduli of continuity of η.