CLT for Lp moduli of continuity of Gaussian processes

AbstractLet G={G(x),x∈R1} be a mean zero Gaussian process with stationary increments and set σ2(|x−y|)=E(G(x)−G(y))2. Let f be a symmetric function with Ef2(η)<∞, where η=N(0,1). When σ2(s) is concave or when σ2(s)=sr, 1<r≤3/2, limh↓0∫abf(G(x+h)−G(x)σ(h))dx−(b−a)Ef(η)Φ(h,σ(h),f,a,b)=lawN(0,1) where Φ(h,σ(h),f,a,b) is the variance of the numerator. This result continues to hold when σ2(s)=sr, 3/2<r