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@article{Street:2021:10.1098/rspa.2020.0957,
author = {Street, OD and Crisan, D},
doi = {10.1098/rspa.2020.0957},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
title = {Semi-martingale driven variational principles},
url = {http://dx.doi.org/10.1098/rspa.2020.0957},
volume = {477},
year = {2021}
}

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TY  - JOUR
AB  - Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a general 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-Poincaré equation can be easily deduced. We show that the deterministic theory is a special case 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.
AU  - Street,OD
AU  - Crisan,D
DO  - 10.1098/rspa.2020.0957
PY  - 2021///
SN  - 1364-5021
TI  - Semi-martingale driven variational principles
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2020.0957
VL  - 477
ER  -

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