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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Brownian motion at a slow point


Authors: Martin T. Barlow and Edwin A. Perkins
Journal: Trans. Amer. Math. Soc. 296 (1986), 741-775
MSC: Primary 60J65; Secondary 60H05, 60J60
MathSciNet review: 846605
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Abstract: If $ c > 1$ there are points $ T(\omega)$ such that the piece of a Brownian path $ B,X(t) = B(T + t) - B(T)$, lies within the square root boundaries $ \pm c\sqrt t $. We study probabilistic and sample path properties of $ X$. In particular, we show that $ X$ is an inhomogeneous Markov process satisfying a certain stochastic differential equation, and we analyze the local behaviour of its local time at zero.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0846605-2
PII: S 0002-9947(1986)0846605-2
Keywords: Brownian motion, slow point, stochastic differential equation, grossissement d'une filtration, local time, stochastic integral
Article copyright: © Copyright 1986 American Mathematical Society