Brownian motion at a slow point

Barlow, Martin T.; Perkins, Edwin A.

doi:10.1090/S0002-9947-1986-0846605-2

Brownian motion at a slow point
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by Martin T. Barlow and Edwin A. Perkins

Trans. Amer. Math. Soc. 296 (1986), 741-775

DOI: https://doi.org/10.1090/S0002-9947-1986-0846605-2

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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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