Approximation d'un mouvement brownien et d'un pont brownien par un processus stationnaire. (Approximation of a Brownian motion and a Brownian bridge by a stationary process) (Q1079301)

The author considers the problem of finding, among the stationary processes, the closest one, in the sense of the Kullback information, to the Brownian motion and to the Brownian bridge. For the Brownian motion the solution is the Ornstein-Uhlenbeck process and for the Brownian bridge it is a particular case of reciprocal process. The results are proved by means of the Girsanov formula and, in the latter case, also by means of the stochastic differential equation associated with the reciprocal process.