Geometry of non-holonomic diffusion

Hochgerner, Simon, and Ratiu, Tudor S.. "Geometry of non-holonomic diffusion." Journal of the European Mathematical Society 017.2 (2015): 273-319. <http://eudml.org/doc/277764>.

@article{Hochgerner2015,
abstract = {We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For $G$-Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.},
author = {Hochgerner, Simon, Ratiu, Tudor S.},
journal = {Journal of the European Mathematical Society},
keywords = {non-holonomic system; symmetry; measure; reduction; diffusion; Brownian motion; generator; Chaplygin system; snakeboard; two-wheeled carriage; non-holonomic system; stochastic dynamics; diffusion; Chaplygin system; Brownian motion},
language = {eng},
number = {2},
pages = {273-319},
publisher = {European Mathematical Society Publishing House},
title = {Geometry of non-holonomic diffusion},
url = {http://eudml.org/doc/277764},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Hochgerner, Simon
AU - Ratiu, Tudor S.
TI - Geometry of non-holonomic diffusion
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 2
SP - 273
EP - 319
AB - We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For $G$-Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.
LA - eng
KW - non-holonomic system; symmetry; measure; reduction; diffusion; Brownian motion; generator; Chaplygin system; snakeboard; two-wheeled carriage; non-holonomic system; stochastic dynamics; diffusion; Chaplygin system; Brownian motion
UR - http://eudml.org/doc/277764
ER -