Lévy flows on manifolds and Lévy processes on Lie groups
For an arbitrary (not necessarily compact) manifold \(M\) the authors consider the problem of constructing the stochastic flow of diffeomorphisms of \(M\) corresponding to a stochastic differential equation (SDE) driven by a Lévy process. The Lévy process driving the SDE is supposed to have finitely many degrees of freedom, so that the Poisson random measure component of the process is itself defined on a finite dimensional manifold \(N\). The authors construct the flow in two particular cases: (i) \(N\) is a Euclidean space, and the Lie algebra generated by the vector fields driving the SDE is finitely dimensional, and (ii) \(N\) is a finite dimensional Lie group, and the vector fields driving the SDE are left invariant.
scientific article; zbMATH DE number 584585