Inverse first-exit problem for the Wiener process

The following inverse first-exit problem for the Wiener process is considered: to find a domain G such that (0,0) ∈ G ∪ ∂G ⊂ ℝ+ x ℝ and the distribution of the first-exit point from this domain has given properties. Theorems on comparison of densiries and moment characterization of domains are applied in estimating domains with uniform distribution of the first-exit point. Two asymptotics are investigated corresponding to densities uniformly tending to zero and to infinity. ©2000 Kluwer Academic/Plenum Publishers.