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Transportation-cost inequalities for non-linear Gaussian functionals

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  • Ioannis Gasteratos
  • Antoine Jacquier

Abstract

We study concentration properties for laws of non-linear Gaussian functionals on metric spaces. Our focus lies on measures with non-Gaussian tail behaviour which are beyond the reach of Talagrand's classical Transportation-Cost Inequalities (TCIs). Motivated by solutions of Rough Differential Equations and relying on a suitable contraction principle, we prove generalised TCIs for functionals that arise in the theory of regularity structures and, in particular, in the cases of rough volatility and the two-dimensional Parabolic Anderson Model. In doing so, we also extend existing results on TCIs for diffusions driven by Gaussian processes.

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  • Ioannis Gasteratos & Antoine Jacquier, 2023. "Transportation-cost inequalities for non-linear Gaussian functionals," Papers 2310.05750, arXiv.org.
    • Handle: RePEc:arx:papers:2310.05750
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    References listed on IDEAS

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    6. Paul Gassiat, 2018. "On the martingale property in the rough Bergomi model," Papers 1811.10935, arXiv.org, revised Apr 2019.
    7. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
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