CLT for L^{p} moduli of continuity of Gaussian processes
| dc.creator | Marcus, Michael B. | |
| dc.creator | Rosen, Jay | |
| dc.date | 2006-10-29 | |
| dc.date.accessioned | 2026-07-07T07:29:35Z | |
| dc.date.available | 2026-07-07T07:29:35Z | |
| dc.description | Let G=\{G(x),x\in R^1\} be a mean zero Gaussian processes with stationary increments and set \si ^2(|x-y|)= E(G(x)-G(y))^2. Let f be a symmetric function with Ef(η)<\ff, where η=N(0,1). When \si^2(s) is concave or when \si^2(s)=s^r$, $1<r\leq 3/2 we have \lim_{h\downarrow 0}{\int_a^b f(\frac{G(x+h)-G(x)}{\si (h)}) dx - (b-a)Ef(η)\over \sqrt{Φ(h,\si(h),f,a,b)}}= N(0,1) in law where Φ(h,\si(h),f,a,b) is the variance of the numerator. This result continues to hold when \si^2(s)=s^r, 3/2<r<2, for certain functions f, depending on the nature of the coefficients in their Hermite polynomial expansion. The asymptotic behavior of Φ(h,\si(h),f,a,b) at zero, is described in a very large number of cases. | |
| dc.identifier | https://arxiv.org/abs/math/0610894 | |
| dc.identifier | http://arxiv.org/abs/math/0610894 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118165 | |
| dc.subject | Probability | |
| dc.subject | 60F05, 60G15 | |
| dc.title | CLT for L^{p} moduli of continuity of Gaussian processes | |
| dc.type | text |