Existence of martingale solutions for stochastic flocking models with local alignment
Probability
2020-07-06 v1
Abstract
We establish the existence of martingale solutions to a class of stochastic conservation equations. The underlying models correspond to random perturbations of kinetic models for collective motion such as the Cucker-Smale and Motsch-Tadmor models. By regularizing the coefficients, we first construct approximate solutions obtained as the mean-field limit of the corresponding particle systems. We then establish the compactness in law of this family of solutions by relying on a stochastic averaging lemma. This extends the results obtained by Karper, Mellet and Trivisa in the deterministic case.
Cite
@article{arxiv.2007.01512,
title = {Existence of martingale solutions for stochastic flocking models with local alignment},
author = {Arnaud Debussche and Angelo Rosello},
journal= {arXiv preprint arXiv:2007.01512},
year = {2020}
}