Fractional Diffusion Bridges
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908683702632448 |
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| author | Inahama, Yuzuru |
| author_facet | Inahama, Yuzuru |
| contents | Consider ``stochastic differential equations" driven by fractional Brownian motion with Hurst parameter H (1/4 <H< 1). Their solutions are sometimes called fractional diffusion processes. The main purpose of this paper is conditioning these processes to reach a given terminal point. We call the conditioned processes fractional diffusion bridges. Our main tool for mathematically rigorous conditioning is quasi-sure analysis, which is a potential theoretic part of Malliavin calculus. We also prove a small-noise large deviation principle of Freidlin-Wentzell type for scaled fractional diffusion bridges under a mild ellipticity assumption on the coefficient vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01197 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Diffusion Bridges Inahama, Yuzuru Probability 60L20, 60H07, 60G22, 60F10 Consider ``stochastic differential equations" driven by fractional Brownian motion with Hurst parameter H (1/4 <H< 1). Their solutions are sometimes called fractional diffusion processes. The main purpose of this paper is conditioning these processes to reach a given terminal point. We call the conditioned processes fractional diffusion bridges. Our main tool for mathematically rigorous conditioning is quasi-sure analysis, which is a potential theoretic part of Malliavin calculus. We also prove a small-noise large deviation principle of Freidlin-Wentzell type for scaled fractional diffusion bridges under a mild ellipticity assumption on the coefficient vector fields. |
| title | Fractional Diffusion Bridges |
| topic | Probability 60L20, 60H07, 60G22, 60F10 |
| url | https://arxiv.org/abs/2512.01197 |