Semi-martingale driven variational principles

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