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| Main Authors: | , |
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| Format: | Preprint |
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2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2011.14151 |
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| _version_ | 1866929337255591936 |
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| author | Kennerberg, Philip Wiktorsson, Magnus |
| author_facet | Kennerberg, Philip Wiktorsson, Magnus |
| contents | We show that non continuous Dirichlet processes, defined as in \cite{NonCont} are closed under a wide family of locally Lipschitz continuous maps (similar to the time-homogeneous variants of the maps considered in \cite{Low}) thus extending Theorem 2.1. from that paper. We provide an Itô formula for these transforms and apply it to study of how $[f(X^n)-f(X)]\to 0$ when $X^n\to X$ (in some appropriate sense) for certain Dirichlet processes $\{X^n\}_n$, $X$ and certain locally Lipschitz continuous maps. We also consider how $[f_n(X^n)-f(X)]\to 0$ for $C^1$ maps $\{f_n\}_n$, $f$ when $f_n'\to f'$ uniformly on compacts. For applications we give examples of jump removal and stability of integrators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_14151 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Stability in quadratic variation, with applications Kennerberg, Philip Wiktorsson, Magnus Probability We show that non continuous Dirichlet processes, defined as in \cite{NonCont} are closed under a wide family of locally Lipschitz continuous maps (similar to the time-homogeneous variants of the maps considered in \cite{Low}) thus extending Theorem 2.1. from that paper. We provide an Itô formula for these transforms and apply it to study of how $[f(X^n)-f(X)]\to 0$ when $X^n\to X$ (in some appropriate sense) for certain Dirichlet processes $\{X^n\}_n$, $X$ and certain locally Lipschitz continuous maps. We also consider how $[f_n(X^n)-f(X)]\to 0$ for $C^1$ maps $\{f_n\}_n$, $f$ when $f_n'\to f'$ uniformly on compacts. For applications we give examples of jump removal and stability of integrators. |
| title | Stability in quadratic variation, with applications |
| topic | Probability |
| url | https://arxiv.org/abs/2011.14151 |