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arXiv · 2310.05750

Transportation-cost inequalities for non-linear Gaussian functionals

Ioannis Gasteratos·Antoine Jacquier
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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. 2023-10-09. Transportation-cost inequalities for non-linear Gaussian functionals. https://arxiv.org/abs/2310.05750

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