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February, 1983 Brownian Motion with Lower Class Moving Boundaries Which Grow Faster Than $t^{1/2}$
R. F. Bass, M. Cranston
Ann. Probab. 11(1): 34-39 (February, 1983). DOI: 10.1214/aop/1176993657

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

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R. F. Bass. M. Cranston. "Brownian Motion with Lower Class Moving Boundaries Which Grow Faster Than $t^{1/2}$." Ann. Probab. 11 (1) 34 - 39, February, 1983. https://doi.org/10.1214/aop/1176993657

Information

Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0503.60080
MathSciNet: MR682798
Digital Object Identifier: 10.1214/aop/1176993657

Subjects:
Primary: 60J65
Secondary: 60G40 , 60J15

Keywords: Brownian motion , moving boundaries , Random walks

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 1 • February, 1983
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