## The Annals of Probability

### Brownian Motion with Lower Class Moving Boundaries Which Grow Faster Than $t^{1/2}$

#### Abstract

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 $(2t \ln \ln t)^{1/2}$.

#### Article information

Source
Ann. Probab., Volume 11, Number 1 (1983), 34-39.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993657

Digital Object Identifier
doi:10.1214/aop/1176993657

Mathematical Reviews number (MathSciNet)
MR682798

Zentralblatt MATH identifier
0503.60080

JSTOR
Bass, R. F.; Cranston, M. Brownian Motion with Lower Class Moving Boundaries Which Grow Faster Than $t^{1/2}$. Ann. Probab. 11 (1983), no. 1, 34--39. doi:10.1214/aop/1176993657. https://projecteuclid.org/euclid.aop/1176993657