Transportation distances and noise sensitivity of multiplicative L\'evy SDE with applications

Abstract

This article assesses the distance between the laws of stochastic differential equations with multiplicative L\'evy noise on path space in terms of their characteristics. The notion of transportation distance on the set of L\'evy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.