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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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