کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590133 | 1334936 | 2014 | 48 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On continuity equations in infinite dimensions with non-Gaussian reference measure On continuity equations in infinite dimensions with non-Gaussian reference measure](/preview/png/4590133.png)
Let γ be a Gaussian measure on a locally convex space and H be the corresponding Cameron–Martin space. It has been recently shown by L. Ambrosio and A. Figalli that the linear first-order PDEρ˙+divγ(ρ⋅b)=0,ρ|t=0=ρ0, where ρ0⋅γρ0⋅γ is a probability measure, admits a weak solution, in particular, under the following assumptions:‖b‖H∈Lp(γ),p>1,exp(ε(divγb)−)∈L1(γ). Applying transportation of measures via triangular maps we prove a similar result for a large class of non-Gaussian probability measures ν on R∞R∞, under the main assumption that βi∈⋂n∈NLn(ν)βi∈⋂n∈NLn(ν) for every i∈Ni∈N, where βiβi is the logarithmic derivative of ν along the coordinate xixi. 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.
Journal: Journal of Functional Analysis - Volume 266, Issue 7, 1 April 2014, Pages 4490–4537