Karhunen-Loève expansions of mean-centered Wiener processes
| dc.creator | Deheuvels, Paul | |
| dc.date | 2006-12-22 | |
| dc.date.accessioned | 2026-07-07T07:36:51Z | |
| dc.date.available | 2026-07-07T07:36:51Z | |
| dc.description | For $γ>-{1/2}$, we provide the Karhunen-Loève expansion of the weighted mean-centered Wiener process, defined by \[W _γ(t)=\frac{1}{\sqrt{1+2γ}}\Big\{W\big(t^{1+2γ}\big)- \int_0^1W\big(u^{1+2γ}\big)du\Big\},\] for $t\in(0,1]$. We show that the orthogonal functions in these expansions have simple expressions in term of Bessel functions. Moreover, we obtain that the $L^2[0,1]$ norm of $W_γ$ is identical in distribution with the $L^2[0,1]$ norm of the weighted Brownian bridge $t^γB(t)$. | |
| dc.description | Published at http://dx.doi.org/10.1214/074921706000000761 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0612693 | |
| dc.identifier | http://arxiv.org/abs/math/0612693 | |
| dc.identifier | IMS Lecture Notes Monograph Series 2006, Vol. 51, 62-76 | |
| dc.identifier | doi:10.1214/074921706000000761 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120574 | |
| dc.subject | Probability | |
| dc.subject | 62G10 (Primary) 60F15, 60G15, 60H07, 62G30 (Secondary) | |
| dc.title | Karhunen-Loève expansions of mean-centered Wiener processes | |
| dc.type | text |