Nonparametric Estimation of the Transition Density Function for Diffusion Processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916713220538368 |
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| author | Comte, Fabienne Marie, Nicolas |
| author_facet | Comte, Fabienne Marie, Nicolas |
| contents | We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under conditions on the diffusion coefficients ensuring that this quantity exists. We use a least squares projection method on a product of finite dimensional spaces, prove risk bounds for the estimator and propose an anisotropic model selection method, relying on several reference norms. A simulation study illustrates the theoretical part for Ornstein-Uhlenbeck or square-root (Cox-Ingersoll-Ross) processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonparametric Estimation of the Transition Density Function for Diffusion Processes Comte, Fabienne Marie, Nicolas Statistics Theory We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under conditions on the diffusion coefficients ensuring that this quantity exists. We use a least squares projection method on a product of finite dimensional spaces, prove risk bounds for the estimator and propose an anisotropic model selection method, relying on several reference norms. A simulation study illustrates the theoretical part for Ornstein-Uhlenbeck or square-root (Cox-Ingersoll-Ross) processes. |
| title | Nonparametric Estimation of the Transition Density Function for Diffusion Processes |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2404.00157 |