Regularity and stability for the Gibbs conditioning principle on path space via McKean-Vlasov control

We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for the optimal solutions in the associated version of the Gibbs conditioning principle. The proofs rely on the analysis of a McKean-Vlasov control problem with distributional constraints. Some new estimates are derived for Hamilton-Jacobi-Bellman equations and the Hessian of the log-density of diffusion processes, which are of independent interest.

• Publication year

  2024

• Venue

  Probability theory and related fields

• Publication date

  2024-10-30

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1007/s00440-025-01447-9arXiv 2410.23016
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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