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Regular version of the site

Article

On continuity equations in infinite dimensions with non-Gaussian reference measure

Journal of Functional Analysis. 2014. Vol. 266. No. 7. P. 4490-4537.
Kolesnikov A., Roeckner M.

Let γ be a Gaussian measure on a locally convex space X and H be the corresponding Cameron-Martin space. It has been recently shown by L. Ambrosio and A. Figalli that the linear first-order transportational PDE  on X admits a weak solution  under broad assumptions.  Applying transportation of measures via triangular maps we prove a similar result for a large class of non-Gaussian probability measures ν on $\R^{\infty}$, under the main assumption of integrability of logarithmic derivativesof v. We also show uniqueness of the solution for a wide class of measures. This class includes uniformly log-concave Gibbs measures and certain product measures. measures.