Non-parametric Inference for Diffusion Processes: A Computational Approach via Bayesian Inversion for PDEs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909377161592832 |
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| author | Kruse, Maximilian Krumscheid, Sebastian |
| author_facet | Kruse, Maximilian Krumscheid, Sebastian |
| contents | In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations arising from the infinitesimal generator of the underlying process. Following a problem formulation in the infinite-dimensional setting, we discuss optimization- and sampling-based solution methods. As preliminary results, we showcase the inference of a single-scale, as well as a multiscale process from trajectory data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-parametric Inference for Diffusion Processes: A Computational Approach via Bayesian Inversion for PDEs Kruse, Maximilian Krumscheid, Sebastian Computational Engineering, Finance, and Science Computation In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations arising from the infinitesimal generator of the underlying process. Following a problem formulation in the infinite-dimensional setting, we discuss optimization- and sampling-based solution methods. As preliminary results, we showcase the inference of a single-scale, as well as a multiscale process from trajectory data. |
| title | Non-parametric Inference for Diffusion Processes: A Computational Approach via Bayesian Inversion for PDEs |
| topic | Computational Engineering, Finance, and Science Computation |
| url | https://arxiv.org/abs/2411.02324 |