There is presently no solution to the problem of characterizing the st
atistics of trapping of a one-dimensional Brownian particle that moves
between two traps, when velocity is relevant. We analyze a simplified
version of this problem in which the continuous velocity is replaced
by three velocities, +/-upsilon and 0, allowing the particle to make r
andom transitions between these states. This model is easily solved an
d exhibits turnover behavior as a function of the noise intensity (i.e
., the jump rate). (C) 1998 Elsevier Science B.V. All rights reserved.