Short time expansion for first passage distributions
Reuven Zeitak · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997
The probability that a stationary correlated Gaussian process does not cross zero in an interval of length $t$ is computed to fifth order in $t$ by a short time expansion. The difficulties inherent in finding higher order terms are discussed. The expansion is tested by simulations and comparison to some approximate results.