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Parameter Estimation in Nonlinear Multivariate Stochastic Differential Equations Based on Splitting Schemes. A preprint

The Annals of statistics, 2024 [Peer Reviewed Journal]

Distributed under a Creative Commons Attribution 4.0 International License ;ISSN: 0090-5364 ;EISSN: 2168-8966 ;DOI: 10.48550/arXiv.2211.11884

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  • Title:
    Parameter Estimation in Nonlinear Multivariate Stochastic Differential Equations Based on Splitting Schemes. A preprint
  • Author: Pilipovic, Predrag ; Samson, Adeline ; Ditlevsen, Susanne
  • Subjects: Mathematics
  • Is Part Of: The Annals of statistics, 2024
  • Description: Surprisingly, general estimators for nonlinear continuous time models based on stochastic differential equations are yet lacking. Most applications still use the Euler-Maruyama discretization, despite many proofs of its bias. More sophisticated methods, such as Kessler's Gaussian approximation, Ozak's Local Linearization, Aït-Sahalia's Hermite expansions, or MCMC methods, lack a straightforward implementation, do not scale well with increasing model dimension or can be numerically unstable. We propose two efficient and easy-to-implement likelihood-based estimators based on the Lie-Trotter (LT) and the Strang (S) splitting schemes. We prove that S has L p convergence rate of order 1, a property already known for LT. We show that the estimators are consistent and asymptotically efficient under the less restrictive one-sided Lipschitz assumption. A numerical study on the 3-dimensional stochastic Lorenz system complements our theoretical findings. The simulation shows that the S estimator performs the best when measured on precision and computational speed compared to the state-of-the-art.
  • Publisher: Institute of Mathematical Statistics
  • Language: English
  • Identifier: ISSN: 0090-5364
    EISSN: 2168-8966
    DOI: 10.48550/arXiv.2211.11884
  • Source: Hyper Article en Ligne (HAL) (Open Access)
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