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Kinetic interacting particle system: Parameter estimation from complete and partial discrete observations

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  • Amorino, Chiara
  • Pilipauskaitė, Vytautė

Abstract

In this paper, we study the estimation of drift and diffusion coefficients in a two-dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial discrete observation cases over a fixed time horizon [0, T] and propose novel contrast functions for parameter estimation. In the partial observation scenario, we tackle the challenge posed by unobserved velocities by introducing a surrogate process based on the increments of the observed positions. This requires a modified contrast function to account for the correlation between successive increments.

Suggested Citation

  • Amorino, Chiara & Pilipauskaitė, Vytautė, 2026. "Kinetic interacting particle system: Parameter estimation from complete and partial discrete observations," Stochastic Processes and their Applications, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:spapps:v:200:y:2026:i:c:s0304414926001523
    DOI: 10.1016/j.spa.2026.105020
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    References listed on IDEAS

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    1. Susanne Ditlevsen & Adeline Samson, 2019. "Hypoelliptic diffusions: filtering and inference from complete and partial observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 361-384, April.
    2. Chiara Amorino & Arnaud Gloter, 2020. "Contrast function estimation for the drift parameter of ergodic jump diffusion process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 279-346, June.
    3. Samson, Adeline & Thieullen, Michèle, 2012. "A contrast estimator for completely or partially observed hypoelliptic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2521-2552.
    4. Della Maestra, Laetitia & Hoffmann, Marc, 2023. "The LAN property for McKean–Vlasov models in a mean-field regime," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 109-146.
    5. Yasutaka Shimizu, 2006. "M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 179-225, July.
    6. Amorino, Chiara & Heidari, Akram & Pilipauskaitė, Vytautė & Podolskij, Mark, 2023. "Parameter estimation of discretely observed interacting particle systems," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 350-386.
    7. Yvo Pokern & Andrew M. Stuart & Petter Wiberg, 2009. "Parameter estimation for partially observed hypoelliptic diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 49-73, January.
    8. Iguchi, Yuga & Beskos, Alexandros & Graham, Matthew M., 2024. "Parameter inference for degenerate diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    9. Wen, Jianghui & Wang, Xiangjun & Mao, Shuhua & Xiao, Xinping, 2016. "Maximum likelihood estimation of McKean–Vlasov stochastic differential equation and its application," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 237-246.
    10. Sharrock, Louis & Kantas, Nikolas & Parpas, Panos & Pavliotis, Grigorios A., 2023. "Online parameter estimation for the McKean–Vlasov stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 481-546.
    11. Chiara Amorino & Arnaud Gloter, 2021. "Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function," Statistical Inference for Stochastic Processes, Springer, vol. 24(1), pages 61-148, April.
    12. Genon-Catalot, Valentine & Larédo, Catherine, 2021. "Probabilistic properties and parametric inference of small variance nonlinear self-stabilizing stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 513-548.
    13. Anna Melnykova, 2020. "Parametric inference for hypoelliptic ergodic diffusions with full observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 595-635, October.
    14. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    15. Wu, Liming, 2001. "Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 205-238, February.
    16. Arnaud Gloter, 2006. "Parameter Estimation for a Discretely Observed Integrated Diffusion Process," Post-Print hal-00404901, HAL.
    17. Pilipovic, Predrag & Samson, Adeline & Ditlevsen, Susanne, 2025. "Strang splitting for parametric inference in second-order stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 187(C).
    18. Arnaud Gloter, 2006. "Parameter Estimation for a Discretely Observed Integrated Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 83-104, March.
    19. Susanne Ditlevsen & Michael Sørensen, 2004. "Inference for Observations of Integrated Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 417-429, September.
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