A closed formula for the mean of a maximum likelihood estimator associated with the Brownian bridge is obtained; the exact relation with that of the Brownian motion is established.
"The Mean of a Maximum Likelihood Estimator Associated with the Brownian Bridge." Electron. Commun. Probab. 8 1 - 5, 2003. https://doi.org/10.1214/ECP.v8-1064