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Brownian motion with a drift in a Poissonian potential. (English) Zbl 0814.60021
The author studies the long time behaviour of a $$d$$-dimensional Brownian motion $$\{Z_ t\}$$ with a constant drift $$h$$ if the original Wiener measure is exponentially weighted with respect to a Poissonian potential. It turns out that the sample path behaviour of $$\{Z_ t\}$$ under the weighted probability measure is substantially different for the two cases of small and large $$h$$, respectively. Precise asymptotics are derived for small $$h$$ whereas lower bounds are established for the case of large $$h$$.

##### MSC:
 60F10 Large deviations 60J65 Brownian motion 60G17 Sample path properties
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##### References:
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