Characteristics and It{ô}'s formula for weak Dirichlet processes: an equivalence result
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929435049984000 |
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| author | Bandini, Elena Russo, Francesco |
| author_facet | Bandini, Elena Russo, Francesco |
| contents | The main objective consists in generalizing a well-known It{ô} formula of J. Jacod and A. Shiryaev: given a c{à}dl{à}g process S, there is an equivalence between the fact that S is a semimartingale with given characteristics (B^k , C, $ν$) and a It{ô} formula type expansion of F (S), where F is a bounded function of class C2. This result connects weak solutions of path-dependent SDEs and related martingale problems. We extend this to the case when S is a weak Dirichlet process. A second aspect of the paper consists in discussing some untreated features of stochastic calculus for finite quadratic variation processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristics and It{ô}'s formula for weak Dirichlet processes: an equivalence result Bandini, Elena Russo, Francesco Probability The main objective consists in generalizing a well-known It{ô} formula of J. Jacod and A. Shiryaev: given a c{à}dl{à}g process S, there is an equivalence between the fact that S is a semimartingale with given characteristics (B^k , C, $ν$) and a It{ô} formula type expansion of F (S), where F is a bounded function of class C2. This result connects weak solutions of path-dependent SDEs and related martingale problems. We extend this to the case when S is a weak Dirichlet process. A second aspect of the paper consists in discussing some untreated features of stochastic calculus for finite quadratic variation processes. |
| title | Characteristics and It{ô}'s formula for weak Dirichlet processes: an equivalence result |
| topic | Probability |
| url | https://arxiv.org/abs/2407.17071 |