Brownian approximations to first passage probabilities

Summary By direct probabilistic argument one term of an Edgeworth type asymptotic expansion is obtained for certain first passage distributions for random walks. These results provide partial justification for and extensions of approximations suggested earlier as a heuristic consequence of Laplace transform calculations.Research supported by ONR Contract N00014-77-C-0306, NSF Grant MCS77-16974, and by the Humboldt Stiftung