Parameter Estimation in Nonlinear Multivariate Stochastic Differential Equations Based on Splitting Schemes. A preprint - Archive ouverte HAL Access content directly
Journal Articles Annals of Statistics Year : 2024

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

Abstract

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.
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Dates and versions

hal-04457892 , version 1 (14-02-2024)
hal-04457892 , version 2 (13-03-2024)

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Predrag Pilipovic, Adeline Samson, Susanne Ditlevsen. Parameter Estimation in Nonlinear Multivariate Stochastic Differential Equations Based on Splitting Schemes. A preprint. Annals of Statistics, inPress, ⟨10.48550/arXiv.2211.11884⟩. ⟨hal-04457892v2⟩
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