Almost Sure Convergence of Uniform Transport Processes to Brownian Motion
Griego, Richard J. ; Heath, David ; Ruiz-Moncayo, Alberto
Ann. Math. Statist., Tome 42 (1971) no. 6, p. 1129-1131 / Harvested from Project Euclid
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Let $x_n(t)$ be the position of a particle in one dimension that switches between uniform velocities $+n$ and $-n$ at the jump times of a Poisson process with intensity $n^2$. In this note are constructed realizations of the processes $x_n(t)$ that converge almost surely to Brownian motion, uniformly on the unit time interval.
Publié le : 1971-06-14
Classification:  
@article{1177693346,
     author = {Griego, Richard J. and Heath, David and Ruiz-Moncayo, Alberto},
     title = {Almost Sure Convergence of Uniform Transport Processes to Brownian Motion},
     journal = {Ann. Math. Statist.},
     volume = {42},
     number = {6},
     year = {1971},
     pages = { 1129-1131},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177693346}
}

Griego, Richard J.; Heath, David; Ruiz-Moncayo, Alberto. Almost Sure Convergence of Uniform Transport Processes to Brownian Motion. Ann. Math. Statist., Tome 42 (1971) no. 6, pp.  1129-1131. http://gdmltest.u-ga.fr/item/1177693346/