Caputo fractional stochastic differential equations: Lipschitz continuity in the fractional order
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909634124578816 |
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| author | Son, T. C. Dung, N. T. Thuy, P. T. P Cuong, T. M. Thao, H. T. P. Tung, P. D. |
| author_facet | Son, T. C. Dung, N. T. Thuy, P. T. P Cuong, T. M. Thao, H. T. P. Tung, P. D. |
| contents | In this paper, we consider a class of the Caputo fractional stochastic differential equations of fractional order $α\in (\frac{1}{2},1]$. Our aim is to analyze of the continuous dependence of solutions on the fractional order $α.$ We first provide explicit estimates for the rate of weak convergence the solutions. We then describe the exact asymptotic behavior of this convergence to show that the rate is optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19965 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Caputo fractional stochastic differential equations: Lipschitz continuity in the fractional order Son, T. C. Dung, N. T. Thuy, P. T. P Cuong, T. M. Thao, H. T. P. Tung, P. D. Probability 26A33, 60J70, 60H07 In this paper, we consider a class of the Caputo fractional stochastic differential equations of fractional order $α\in (\frac{1}{2},1]$. Our aim is to analyze of the continuous dependence of solutions on the fractional order $α.$ We first provide explicit estimates for the rate of weak convergence the solutions. We then describe the exact asymptotic behavior of this convergence to show that the rate is optimal. |
| title | Caputo fractional stochastic differential equations: Lipschitz continuity in the fractional order |
| topic | Probability 26A33, 60J70, 60H07 |
| url | https://arxiv.org/abs/2412.19965 |