Limit laws for Brownian motion conditioned to reach a high level
A functional limit theorem is presented for the behaviour of Brownian motion conditioned to reach a high level during a fixed time interval. The asymptotic behaviour of the conditioned path as the level tends to infinity is expressed via a time reversal and suitable renormalisation of space and time. Some relations to Williams' path decomposition is pointed out.
asymptotic behaviour of the conditioned path
scientific article; zbMATH DE number 178024