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Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications

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  • Gairing, Jan
  • Högele, Michael
  • Kosenkova, Tetiana

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.

Suggested Citation

  • Gairing, Jan & Högele, Michael & Kosenkova, Tetiana, 2018. "Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2153-2178.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:7:p:2153-2178
    DOI: 10.1016/j.spa.2017.09.003
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    References listed on IDEAS

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    1. Imkeller, P. & Pavlyukevich, I., 2006. "First exit times of SDEs driven by stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 611-642, April.
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