Equations driven by fast-oscillating functions of an Itô diffusion process
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910251053219840 |
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| author | Reese, Tanner Wehr, Jan |
| author_facet | Reese, Tanner Wehr, Jan |
| contents | We study Itô SDE systems driven by oscillating functions of a single Itô diffusion process. In the limit when oscillations become fast, we show that the solution process converges in law to the process defined by an SDE system driven by a multivariate Wiener process whose covariance we calculate explicitly. Interestingly, the limiting system of SDEs are most naturally stated using the Stratonovich integral. The problem has been originally motivated by experimental work and special cases of theorems proved here provide a rigorous treatment of equations arising from physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01618 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equations driven by fast-oscillating functions of an Itô diffusion process Reese, Tanner Wehr, Jan Probability Mathematical Physics 60H10, 70Lxx, 60G53 We study Itô SDE systems driven by oscillating functions of a single Itô diffusion process. In the limit when oscillations become fast, we show that the solution process converges in law to the process defined by an SDE system driven by a multivariate Wiener process whose covariance we calculate explicitly. Interestingly, the limiting system of SDEs are most naturally stated using the Stratonovich integral. The problem has been originally motivated by experimental work and special cases of theorems proved here provide a rigorous treatment of equations arising from physics. |
| title | Equations driven by fast-oscillating functions of an Itô diffusion process |
| topic | Probability Mathematical Physics 60H10, 70Lxx, 60G53 |
| url | https://arxiv.org/abs/2312.01618 |