A CLT for the L^{2} modulus of continuity of Brownian local time
| dc.creator | Chen, Xia | |
| dc.creator | Li, Wenbo | |
| dc.creator | Marcus, Michael B. | |
| dc.creator | Rosen, Jay | |
| dc.date | 2009-01-08 | |
| dc.date.accessioned | 2026-07-07T12:27:40Z | |
| dc.date.available | 2026-07-07T12:27:40Z | |
| dc.description | Let $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$ denote the local time of Brownian motion and \[ α_{t}:=\int_{-\infty}^{\infty} (L^{x}_{t})^{2} dx . \] Let $η=N(0,1)$ be independent of $α_{t}$. For each fixed $t$ \[ {\int_{-\infty}^{\infty} (L^{x+h}_{t}- L^{x}_{t})^{2} dx- 4ht\over h^{3/2}} \stackrel{\mathcal{L}}{\to}({64 \over 3})^{1/2}\sqrt{α_{t}} η, \] as $h\rar 0$. Equivalently \[ {\int_{-\infty}^{\infty} (L^{x+1}_{t}- L^{x}_{t})^{2} dx- 4t\over t^{3/4}} \stackrel{\mathcal{L}}{\to}({64 \over 3} )^{1/2}\sqrt{α_{1}} η, \] as $t\rar\infty$. | |
| dc.identifier | https://arxiv.org/abs/0901.1102 | |
| dc.identifier | http://arxiv.org/abs/0901.1102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215282 | |
| dc.subject | Probability | |
| dc.title | A CLT for the L^{2} modulus of continuity of Brownian local time | |
| dc.type | text |