In this article,we prove that nonlinear resolvents of infinitesimal generators on bounded and convex subdomains of \({\mathbb {C}}^n\) are decreasing Loewner chains. Furthermore, we consider the problem of the existence of nonlinear resolvents on unbounded convex domains in \({\mathbb {C}}\) . In the case of the upper half-plane, we obtain a complete solution by using that nonlinear resolvents of certain generators correspond to semigroups of probability measures with respect to free convolution.
