Adaptive Bayes estimator for stochastic differential equations with jumps under small noise asymptotics
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908173291487232 |
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| author | Suzuki, Shuntaro Wakamatsu, Takaaki Shimizu, Yasutaka |
| author_facet | Suzuki, Shuntaro Wakamatsu, Takaaki Shimizu, Yasutaka |
| contents | In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term, and jump term, as well as the Poisson intensity and the probability density function of the underlying jump. We propose estimators based on adaptive Bayesian estimation from discrete observations. We demonstrate the consistency and asymptotic normality of the estimators within the framework of small noise asymptotics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Bayes estimator for stochastic differential equations with jumps under small noise asymptotics Suzuki, Shuntaro Wakamatsu, Takaaki Shimizu, Yasutaka Statistics Theory 62M20, 62G20, 62F15 In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term, and jump term, as well as the Poisson intensity and the probability density function of the underlying jump. We propose estimators based on adaptive Bayesian estimation from discrete observations. We demonstrate the consistency and asymptotic normality of the estimators within the framework of small noise asymptotics. |
| title | Adaptive Bayes estimator for stochastic differential equations with jumps under small noise asymptotics |
| topic | Statistics Theory 62M20, 62G20, 62F15 |
| url | https://arxiv.org/abs/2412.20640 |