Connection between deriving bridges and radial parts from multidimensional Ornstein-Uhlenbeck processes

Summary

First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law).  Then we prove that the law of the radial part of the bridge with endpoints zero derived from a special multidimensional Ornstein--Uhlenbeck process equals the law of the bridge with endpoints zero derived from the radial part of the same Ornstein--Uhlenbeck process.  We also construct bridges derived from general multidimensional Ornstein--Uhlenbeck processes.