Construction of a Brownian Path With a Given Minimum

Jean Bertoin, Jim Pitman, Juan Chavez
1999 Electronic Communications in Probability  
We construct a Brownian path conditioned on its minimum value over a fixed time interval by simple transformations of a Brownian bridge. Path transformations have proved useful in the study of Brownian motion and related processes, by providing simple constructions of various conditioned processes such as Brownian bridge, meander and excursion, starting from an unconditioned Brownian motion. As well as providing insight into the structure of these conditioned processes, path constructions
more » ... constructions assist in the computation of various conditional laws of Brownian functionals, and in the simulation of conditioned processes.
doi:10.1214/ecp.v4-1003 fatcat:rw6hs6fw7vghzdael4rhfj7v6m