Riemann-Skorohod and Stratonovich integrals for Gaussian processes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913685947023360 |
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| author | Liu, Yanghui |
| author_facet | Liu, Yanghui |
| contents | In this paper we consider Skorohod and Stratonovich-type integrals in a general setting of Gaussian processes. We show that a conversion formula holds when the covariance functions of the Gaussian process are of finite $ρ$-variation for $ρ\geq 1$ and that the diagonals of covariance functions are of finite $ρ'$-variation for $ρ'\geq 1$ such that $\frac{1}{ρ'}+\frac{1}{2ρ}>1$. The difference between the two types of integrals is identified with a Young integral. We also show that the Skorohod integral is the limit of a $[ρ]$-th order Skorohod-Riemann sum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riemann-Skorohod and Stratonovich integrals for Gaussian processes Liu, Yanghui Probability 60H07, 60L20 In this paper we consider Skorohod and Stratonovich-type integrals in a general setting of Gaussian processes. We show that a conversion formula holds when the covariance functions of the Gaussian process are of finite $ρ$-variation for $ρ\geq 1$ and that the diagonals of covariance functions are of finite $ρ'$-variation for $ρ'\geq 1$ such that $\frac{1}{ρ'}+\frac{1}{2ρ}>1$. The difference between the two types of integrals is identified with a Young integral. We also show that the Skorohod integral is the limit of a $[ρ]$-th order Skorohod-Riemann sum. |
| title | Riemann-Skorohod and Stratonovich integrals for Gaussian processes |
| topic | Probability 60H07, 60L20 |
| url | https://arxiv.org/abs/2502.06983 |