Diffeomorphic flows driven by Levy processes
Abstract
We prove that the stochastic differential equation Ys,t(x) = Ys,s(x) + ∫0t-s f(Ys,s+u(x)) dXs+u, Ys,s(x)=x∈d. driven by a L\'evy process whose paths have finite p-variation almost surely for some p∈[1,2) defines a flow of locally C1-diffeomorphisms provided the vector field f is α-Lipschitz for some α>p. Using a path- wise approach we relax the smoothness condition normally required for a class of discontinuous semi-martingales.
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