Before revision: The inverse first passage time problem asks whether, for a Brownian motion B and a nonnegative random variable \zeta, there exists a time-varying barrier b such that P\{B_s>b(s), \, 0  s  t\}=P\{\zeta>t\}.
After revision: The inverse first passage time problem asks whether, for a Brownian motion B and a nonnegative random variable \zeta, there exists a time-varying barrier b such that P\{B_s>b(s), \, 0  s \leq s\leq t\}=P\{\zeta>t\}.