Pré-Publication, Document De Travail Année : 2025

Weak rough kernel comparison via PPDEs for integrated Volterra processes

Résumé

Motivated by applications in physics (e.g., turbulence intermittency) and financial mathematics (e.g., rough volatility), this paper examines a family of integrated stochastic Volterra processes characterized by a small Hurst parameter $H<\tfrac{1}{2}$. We investigate the impact of kernel approximation on the integrated process by examining the resulting weak error. Our findings quantify this error in terms of the $L^1$ norm of the difference between the two kernels, as well as the $L^1$ norm of the difference of the squares of these kernels. Our analysis is based on a path-dependent Feynman-Kac formula and the associated partial differential equation (PPDE), providing a robust and extendible framework for our analysis.

Dates et versions

hal-04885861 , version 1 (14-01-2025)

Identifiants

Citer

Mireille Bossy, Kerlyns Martínez Rodríguez, Paul Maurer. Weak rough kernel comparison via PPDEs for integrated Volterra processes. 2025. ⟨hal-04885861⟩
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