On Behrens–Fisher problem for continuous time Gaussian processes Original Research Article

Our setting is the sequential observation of two continuous time multidimensional Gaussian processes whose mean vectors depend linearly on two multidimensional parameters and with different conditions about their covariance structures that will always include nuisance parameters. We analyze the Behrens–Fisher problem of comparing both parameters by means of a confidence set for their difference, with given confidence level and diameter. The random time needed to achieve this goal is also inspected.