Weak rough kernel comparison via PPDEs for integrated Volterra processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913666449801216 |
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| author | Bossy, Mireille Martinez, Kerlyns Maurer, Paul |
| author_facet | Bossy, Mireille Martinez, Kerlyns Maurer, Paul |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_07509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak rough kernel comparison via PPDEs for integrated Volterra processes Bossy, Mireille Martinez, Kerlyns Maurer, Paul Probability 60G22, 60H20, 60H30, 60G15, 35K10 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. |
| title | Weak rough kernel comparison via PPDEs for integrated Volterra processes |
| topic | Probability 60G22, 60H20, 60H30, 60G15, 35K10 |
| url | https://arxiv.org/abs/2501.07509 |