Brownian Motion with Lower Class Moving Boundaries Which Grow Faster Than $t^{1/2}$
Bass, R. F. ; Cranston, M.
Ann. Probab., Tome 11 (1983) no. 4, p. 34-39 / Harvested from Project Euclid
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Upper and lower bounds are obtained for $P(|W(t)| \leq f(t), t \leq u)$ and $P(|S(n)| \leq f(n), n \leq N), u, N$ large, where $W(t)$ is a Brownian motion, $S(n)$ is a random walk with $ES(1) = 0, E|S(1)|^{2+2\eta} < \infty$, and $f(t)$ is a deterministic function growing faster than $t^{1/2}$ but slower than $(2t \ln \ln t)^{1/2}$.
Publié le : 1983-02-14
Classification:  Moving boundaries,  Brownian motion,  random walks,  60J65,  60J15,  60G40 
@article{1176993657,
     author = {Bass, R. F. and Cranston, M.},
     title = {Brownian Motion with Lower Class Moving Boundaries Which Grow Faster Than $t^{1/2}$},
     journal = {Ann. Probab.},
     volume = {11},
     number = {4},
     year = {1983},
     pages = { 34-39},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993657}
}

Bass, R. F.; Cranston, M. Brownian Motion with Lower Class Moving Boundaries Which Grow Faster Than $t^{1/2}$. Ann. Probab., Tome 11 (1983) no. 4, pp.  34-39. http://gdmltest.u-ga.fr/item/1176993657/