In the talk we analyse semimartingale properties of a class of Gauss-
ian periodic processes, called convoluted Brownian motions, obtained by convolution
between a deterministic function and a Brownian motion. A classical example in this
class is the periodic Ornstein-Uhlenbeck process.
We compute their characteristics and show that in general, they are never Markovian
nor satisfy a time-Markov eld property. Nevertheless, by enlargement of ltration
and/or addition of a one-dimensional component, one can in some case recover the
Markovianity. We treat exhaustively the case of the bidimensional trigonometric con-
voluted Brownian motion and the multidimensional monomial convoluted Brownian
motion.