Diffeomorphic flows driven by Levy processes

2000/01/04 by David R. E. Williams, Williams, David R. E.
Mathematics · #60H20 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H20

paper · pdf · doi:10.48550/arxiv.math/0001016

arxiv created 2000/01/04 · arxiv updated 2009/11/30

Abstract

We prove that the stochastic differential equation Y_s,t(x) = Y_s,s(x) + ∫₀^t-s f(Y_s,s+u(x)) dX_s+u, Y_s,s(x)=x∈\R^d. driven by a Lévy 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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