Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications

Jan Gairing, Michael Högele and Tetiana Kosenkova

Stochastic Processes and their Applications, 2018, vol. 128, issue 7, 2153-2178

Abstract: This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Lévy 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.

Keywords: Stochastic differential equations; Multiplicative Lévy noise; Lévy type processes; Heavy-tailed distributions; Model selection; Wasserstein distance; Time series (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2017.09.003

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