Taylor expansions of curve-crossing probabilities
A Taylor expansion is obtained for the probability that a Brownian motion hits a smooth nonlinear boundary of the type \(a+\beta t+\varepsilon c(t)\) for small \(\varepsilon> 0\). The proof is based on the Cameron-Martin-Girsanov formula. A probabilistic interpretation of the expansion is given.
scientific article; zbMATH DE number 1396204