Convergence of stochastic flows with jumps and Lévy processes in diffeomorphisms group (Q1819825)

Let \(\xi^ n_{s,t}\) be a sequence of stochastic flows with jumps generated by a sequence of Levy processes \(X^ n_ t\) with values in the vector space of smooth mappings of \({\mathbb{R}}^ d\). The author gives a criterion that \(\xi^ n_{s,t}\) converges weakly by means of the characteristics of the generators \(X^ n_ t\), \(n=1,2,... \). Also strong convergence of \(\xi^ n_{s,t}\) and \(X^ n_ t\) is considered. As an application the case where a stochastic flow \(\xi_{s,t}\) takes values in diffeomorphisms group of \({\mathbb{R}}^ d\) is studied.