On Stopping Times for $n$ Dimensional Brownian Motion
Davis, Burgess
Ann. Probab., Tome 6 (1978) no. 6, p. 651-659 / Harvested from Project Euclid
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Let $\bar{X}(t) = (X_1(t),\cdots, X_n(t))$ be standard $n$ dimensional Brownian motion. Results of the following nature are proved. If $\tau$ is a stopping time for $\bar{X}(t)$ then $|\bar{X}(\tau)|$ and $(n\tau)^{\frac{1}{2}}$ are relatively close in $L^p$ if $n$ is large. Also, if $n$ is large most of the moments $EX_i(\tau)^k, i = 1,2,\cdots, n$, are about what they would be if $\bar{X}(t)$ were independent of $\tau$.
Publié le : 1978-08-14
Classification:  Brownian motion,  stopping time,  Bessel process,  60J65,  60J40,  31B05 
@article{1176995485,
     author = {Davis, Burgess},
     title = {On Stopping Times for $n$ Dimensional Brownian Motion},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 651-659},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995485}
}

Davis, Burgess. On Stopping Times for $n$ Dimensional Brownian Motion. Ann. Probab., Tome 6 (1978) no. 6, pp.  651-659. http://gdmltest.u-ga.fr/item/1176995485/