  We examine Jordan-Brans-Dicke theories with a linear potential for the scalar
field by means of a stochastic approach. The backreaction of the scalar field
fluctuations on the classical background is described. The analysis is
concentrated on those values of the Jordan-Brans-Dicke parameter which predict
a superinflationary pre-big-bang branch. The graceful exit problem present in
these theories is discussed.
