Transportation distances and noise sensitivity of multiplicative Levy SDE with applications

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Gairing, Jan¹  Hoegele, Michael²  Kosenkova, Tetiana³ 

[1] Humboldt Univ, Inst Math, Berlin, Germany

[2] Univ Los Andes, Dept Matemat, Bogota, Colombia

[3] Univ Potsdam, Inst Math, Potsdam, Germany

关键词: Stochastic differential equations;    Multiplicative Levy noise;    Levy type processes;    Heavy-tailed distributions;    Model selection;    Wasserstein distance;    Time series;   

DOI  :  10.1016/j.spa.2017.09.003

来源: Elsevier

【 摘 要 】

This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy 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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free