  For a stochastic process with state space some Polish space, this paper gives
sufficient conditions on the initial and conditional distributions for the
joint law to satisfy Gaussian concentration inequalities, transportation
inequalities and also logarithmic Sobolev inequalities in the case of the
Euclidean space. In several cases, the obtained constants are of optimal order
of growth with respect to the number of variables, or are independent of this
number. These results extend results known for mutually independent variables
to weakly dependent variables under Dobrushin-Shlosman type conditions.
