  Spearheaded by the recent efforts to derive stochastic geophysical fluid
dynamics models, we present a generic framework for introducing stochasticity
into variational principles through the concept of a semi-martingale driven
variational principle and constraining the component variables to be compatible
with the driving semi-martingale. Within this framework and the corresponding
choice of constraints, the Euler-Poincare equation can be easily deduced. We
show that their corresponding deterministic counterparts are particular cases
of this class of stochastic variational principles. Moreover, this is a natural
framework that enables us to correctly characterize the pressure term in
incompressible stochastic fluid models. Other general constraints can also be
incorporated as long as they are compatible with the driving semi-martingale.
