Fetching the paper…
Reading the bibliography…
This note shows how to considerably strengthen the usual mode of convergence of an $n$-particle system to its McKean-Vlasov limit, often known as propagation of chaos, when the volatility coefficient is nondegenerate and involves no interaction term.
H.P. McKean, A class of Markov processes associated with nonlinear parabolic equations , Proceedings of the National Academy of Sciences 56
1911
Earlier work this paper cites.
D. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions , Stochastics: An International Journal of Probability and Stochastic Processes 20
1987
Earlier work this paper cites.
J. Gärtner, On the McKean-Vlasov limit for interacting diffusions , Mathematische Nachrichten 137
1988
Earlier work this paper cites.
1991
Earlier work this paper cites.
T.-S. Chiang, McKean-Vlasov equations with discontinuous coefficients , Soochow J. Math 20
1994
Earlier work this paper cites.
D. Bertsekas and S. Shreve, Stochastic optimal control: The discrete time case , Athena Scientific, 1996
1996
Earlier work this paper cites.
M. Bossy and D. Talay, Convergence rate for the approximation of the limit law of weakly interacting particles: application to the Burgers equation , The Annals of Applied Probability 6
1996
Earlier work this paper cites.
B. Jourdain, Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers’ equations , ESAIM: Probability and Statistics 1
1997
Cited alongside, same era.
G.B. Arous and O. Zeitouni, Increasing propagation of chaos for mean field models , Annales de l’Institut Henri Poincare (B) Probability and Statistics, vol. 35, Elsevier, 1999, pp. 85–102
1999
Cited alongside, same era.
J.-M. Lasry and P.-L. Lions, Mean field games , Japanese journal of mathematics 2
2007
Cited alongside, same era.
A. Dembo and O. Zeitouni, Large deviations techniques and applications , vol. 38, Springer Science & Business Media, 2009
2009
Cited alongside, same era.
N. Gozlan and C. Léonard, Transport inequalities. A survey , arXiv preprint arXiv:1003.3852 (2010)
2010
B. Jourdain and J. Reygner, Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation , Stochastic partial differential equations: analysis and computations 1
2013
Later among the works it cites.
V.N. Kolokoltsov, Nonlinear diffusions and stable-like processes with coefficients depending on the median or var , Applied Mathematics & Optimization 68
2013
Later among the works it cites.
D. Crisan, T.G. Kurtz, and Y. Lee, Conditional distributions, exchangeable particle systems, and stochastic partial differential equations , Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 50, Institut Henri Poincaré, 2014, pp. 946–974
2014
Later among the works it cites.
R. Carmona and D. Lacker, A probabilistic weak formulation of mean field games and applications , The Annals of Applied Probability 25
2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
I. Karatzas and S. Shreve, Brownian motion and stochastic calculus , vol. 113, Springer Science & Business Media, 2012
2012
Cited alongside, same era.
M. Shkolnikov, Large systems of diffusions interacting through their ranks , Stochastic Processes and their Applications 122
2012
Cited alongside, same era.
2015
Later among the works it cites.
2016
Later among the works it cites.