$C^{ 0,1}$ -It{ô} chain rules and generalized solutions of parabolic PDEs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908362455646208 |
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| author | Ciccarella, Carlo Russo, Francesco |
| author_facet | Ciccarella, Carlo Russo, Francesco |
| contents | In this paper we first establish an Itô formula for a finite quadratic variation process $X$ expanding $f(t,X_t),$ when $f$ is of class $C^2$ in space and is absolutely continuous in time. Second, via a Fukushima-Dirichlet decomposition we obtain an explicit chain rule for $f(t,X_t)$, when $X$ is a continuous semimartingale and $f$ is a ``quasi-strong solution'' (in the sense of approximation of classical solutions) of a parabolic PDE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^{ 0,1}$ -It{ô} chain rules and generalized solutions of parabolic PDEs Ciccarella, Carlo Russo, Francesco Probability In this paper we first establish an Itô formula for a finite quadratic variation process $X$ expanding $f(t,X_t),$ when $f$ is of class $C^2$ in space and is absolutely continuous in time. Second, via a Fukushima-Dirichlet decomposition we obtain an explicit chain rule for $f(t,X_t)$, when $X$ is a continuous semimartingale and $f$ is a ``quasi-strong solution'' (in the sense of approximation of classical solutions) of a parabolic PDE. |
| title | $C^{ 0,1}$ -It{ô} chain rules and generalized solutions of parabolic PDEs |
| topic | Probability |
| url | https://arxiv.org/abs/2505.08813 |