We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1023,
author = {Yuri E. Gliklikh and Andrei V. Obukhovski\u\i },
title = {Stochastic differential inclusions of Langevin type on Riemannian manifolds},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {21},
year = {2001},
pages = {173-190},
zbl = {1003.58027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1023}
}
Yuri E. Gliklikh; Andrei V. Obukhovskiĭ. Stochastic differential inclusions of Langevin type on Riemannian manifolds. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 21 (2001) pp. 173-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1023/
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