PUB - Publikationen an der Universität Bielefeld

Let gamma 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 PDE div rho + div(gamma)(rho center dot b) = 0, p vertical bar(t=o) = rho o, where rho(o) center dot gamma is a probability measure, admits a weak solution, in particular, under the following assumptions: vertical bar vertical bar b vertical bar vertical bar(H) is an element of L-p (gamma), p > 1, exp(epsilon(div(gamma)b)_) is an element of L-1 (gamma). Applying transportation of measures via triangular maps we prove a similar result for a large class of non-Gaussian probability measures nu on R-infinity, under the main assumption that beta(i) is an element of boolean AND(n is an element of N) L-n(nu) for every i is an element of N, where beta, is the logarithmic derivative of v along the coordinate x(i). 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. (C) 2014 Elsevier Inc. All rights reserved.