Pith. sign in

REVIEW 3 cited by

On the stability of the invariant probability measures of McKean-Vlasov equations

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2201.11612 v4 pith:AUB66MFD submitted 2022-01-27 math.PR math.AP

Quentin Cormier This is my paper · ORCID
classification math.PRmath.AP
keywords stabilityequationsmckean-vlasovconvergenceinteractioninvariantkernelmathbb
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We study the long-time behavior of some McKean-Vlasov stochastic differential equations used to model the evolution of large populations of interacting agents. We give conditions ensuring the local stability of an invariant probability measure. Lions derivatives are used in a novel way to obtain our stability criteria. We obtain results for non-local McKean-Vlasov equations on $\mathbb{R}^d$ and for McKean-Vlasov equations on the torus where the interaction kernel is given by a convolution. On $\mathbb{R}^d$, we prove that the location of the roots of an analytic function determines the stability. On the torus, our stability criterion involves the Fourier coefficients of the interaction kernel. In both cases, we prove the convergence in the Wasserstein metric $W_1$ with an exponential rate of convergence.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Uniform-in-time weak propagation of chaos for consensus-based optimization

    math.OC 2025-02 conditional novelty 7.0 of 10

    For consensus-based optimization on a bounded domain, the particle system's empirical distribution is within O(1/N) of its mean-field limit uniformly in time, and it concentrates about a limit point as N and t grow.

  2. Data-driven approximation of transfer operators for mean-field stochastic differential equations

    math.DS 2025-09 conditional novelty 6.0 of 10

    The authors define Koopman and Perron-Frobenius operators for decoupled McKean-Vlasov SDEs and prove EDMD converges to the projected operators.

  3. Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity

    math.PR 2025-04 conditional novelty 6.0 of 10

    McKean-Vlasov SDEs with pure-jump Lévy noise are shown to have stationary distributions under Lyapunov conditions, multiple such distributions under local dissipativity, and a unique one with exponential convergence u...

Pith tools