  In this paper, we adopt a Bayesian point of view for predicting real
continuous-time processes. We give two equivalent definitions of a Bayesian
predictor and study some properties: admissibility, prediction sufficiency,
non-unbiasedness, comparison with efficient predictors. Prediction of Poisson
process and prediction of Ornstein-Uhlenbeck process in the continuous and
sampled situations are considered. Various simulations illustrate comparison
with non-Bayesian predictors.
