Simulating diffusion bridges using the Wiener chaos expansion
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918138423017472 |
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| author | Delgado-Vences, Francisco Salcedo-Varela, Gabriel Adrián Baltazar-Larios, Fernando |
| author_facet | Delgado-Vences, Francisco Salcedo-Varela, Gabriel Adrián Baltazar-Larios, Fernando |
| contents | In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential equations, and we apply the WCE to a particular representation of the diffusion bridge. Thus, we obtain a method to simulate the proposal diffusion bridges that is fast and that in every attempt constructs a diffusion bridge, which means there are no rejection rates. The method presented in this work could be very useful in statistical inference. We validate the method with a simple Ornstein-Uhlenbeck process. We apply our method to three examples of SDEs and show the numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simulating diffusion bridges using the Wiener chaos expansion Delgado-Vences, Francisco Salcedo-Varela, Gabriel Adrián Baltazar-Larios, Fernando Probability 60Gxx In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential equations, and we apply the WCE to a particular representation of the diffusion bridge. Thus, we obtain a method to simulate the proposal diffusion bridges that is fast and that in every attempt constructs a diffusion bridge, which means there are no rejection rates. The method presented in this work could be very useful in statistical inference. We validate the method with a simple Ornstein-Uhlenbeck process. We apply our method to three examples of SDEs and show the numerical results. |
| title | Simulating diffusion bridges using the Wiener chaos expansion |
| topic | Probability 60Gxx |
| url | https://arxiv.org/abs/2401.06248 |