Abstract
Abstract
We extend the Itô–Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to k-form-valued stochastic processes. The result is the Kunita–Itô–Wentzell (KIW) formula for k-forms. We also establish a correspondence between the KIW formula for k-forms derived here and a certain class of stochastic fluid dynamics models which preserve the geometric structure of deterministic ideal fluid dynamics. This geometric structure includes Eulerian and Lagrangian variational principles, Lie–Poisson Hamiltonian formulations and natural analogues of the Kelvin circulation theorem, all derived in the stochastic setting.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Engineering,Modeling and Simulation
Reference36 articles.
1. Arnaudon, M., Chen, X., Cruzeiro, A.B.: Stochastic Euler–Poincaré reduction. J. Math. Phys. 55(8), 081507 (2014)
2. Arnaudon, A., de Castro, A.L., Holm, D.D.: Noise and dissipation on coadjoint orbits. J. Nonlinear Sci. 28, 91–145 (2018)
3. Arnaudon, A., Holm, D.D., Sommer, S.: A geometric framework for stochastic shape analysis. In: Foundations of Computational Mathematics (FoCM) (2018)
4. Arnaudon, A., Holm, D.D., Sommer, S.: String methods for stochastic image and shape matching. J. Math. Imaging Vis. (JMIV) 60, 953–967 (2018)
5. Arnold, V.I.: Sur un principe variationnel pour les écoulements stationnaires des liquides parfaits et ses applications aux problemes de stabilité non linéaires. J. de mécanique 5(1), 29 (1966)
Cited by
16 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献