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The Absorption Time of a Brownian Motion under One-Sided Controling

by Zierke, E..

Series: 1998-25, Preprints

60J50 Boundary theory
60J65 Brownian motion
60J50 Boundary theory

A Brownian motion with positive drift moves between two barriers. If it reaches the lower barrier, it is immediately reset to a certain fixed level. The upper barrier is absorbing. This paper gives an exact formula of the absorption time of this Brownian motion. In a special case the result is extended to small negative drifts.

Absorbing Barrier, Absorption Time, Brownian Motion