τn = inf{t > 0 : Bi(t)− bi = B0(t) for some 1 ≤ i ≤ n}, where 0 < bi ≤ 1, 1 ≤ i ≤ n. The τn can be viewed as a capture time in a random pursuit setting. Assume that a Brownian prisoner escapes, running along the path of B0. In his pursuit, there are n independent Brownian policemen. These policemen run along the paths of B1, · · · , Bn, respectively. At the outset, the prisoner is ahead of the ...