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Statistical inference for discretely sampled stochastic functional differential equations with small noise

Author

Listed:
  • Hiroki Nemoto

    (Waseda University)

  • Yasutaka Shimizu

    (Waseda University)

Abstract

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast function is based on a local-Gauss approximation to the transition probability density of the process. We show consistency and asymptotic normality of the minimum-contrast estimator when a small dispersion coefficient $$\varepsilon \rightarrow 0$$ ε → 0 and sample size $$n\rightarrow \infty $$ n → ∞ simultaneously.

Suggested Citation

  • Hiroki Nemoto & Yasutaka Shimizu, 2024. "Statistical inference for discretely sampled stochastic functional differential equations with small noise," Statistical Inference for Stochastic Processes, Springer, vol. 27(2), pages 427-456, July.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:2:d:10.1007_s11203-023-09299-7
    DOI: 10.1007/s11203-023-09299-7
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    References listed on IDEAS

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    1. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    2. Gloter, Arnaud & Sørensen, Michael, 2009. "Estimation for stochastic differential equations with a small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 679-699, March.
    3. Long, Hongwei & Shimizu, Yasutaka & Sun, Wei, 2013. "Least squares estimators for discretely observed stochastic processes driven by small Lévy noises," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 422-439.
    4. Peng Wang, 2023. "Risk-Sensitive Maximum Principle for Controlled System with Delay," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
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