Transportation distances and noise sensitivity of multiplicative Levy SDE with applications
- 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.
| Author details: | Jan GairingGND, Michael HögeleORCiDGND, Tetiana KosenkovaORCiD |
|---|---|
| DOI: | https://doi.org/10.1016/j.spa.2017.09.003 |
| ISSN: | 0304-4149 |
| ISSN: | 1879-209X |
| Title of parent work (English): | Stochastic processes and their application |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2017/09/21 |
| Publication year: | 2017 |
| Release date: | 2021/11/17 |
| Tag: | Heavy-tailed distributions; Levy type processes; Model selection; Multiplicative Levy noise; Stochastic differential equations; Time series; Wasserstein distance |
| Volume: | 128 |
| Issue: | 7 |
| Number of pages: | 26 |
| First page: | 2153 |
| Last Page: | 2178 |
| Funding institution: | DFGGerman Research Foundation (DFG) [IRTG 1740]; Potsdam probability group |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
