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arXiv · 2312.04444

Parameter Inference for Hypo-Elliptic Diffusions under a Weak Design Condition

Yuga Iguchi·Alexandros Beskos
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Abstract

We address the problem of parameter estimation for degenerate diffusion processes defined via the solution of Stochastic Differential Equations (SDEs) with diffusion matrix that is not full-rank. For this class of hypo-elliptic diffusions recent works have proposed contrast estimators that are asymptotically normal, provided that the step-size in-between observations $Δ=Δ_n$ and their total number $n$ satisfy $n \to \infty$, $n Δ_n \to \infty$, $Δ_n \to 0$, and additionally $Δ_n = o (n^{-1/2})$. This latter restriction places a requirement for a so-called `rapidly increasing experimental design'. In this paper, we overcome this limitation and develop a general contrast estimator satisfying asymptotic normality under the weaker design condition $Δ_n = o(n^{-1/p})$ for general $p \ge 2$. Such a result has been obtained for elliptic SDEs in the literature, but its derivation in a hypo-elliptic setting is highly non-trivial. We provide numerical results to illustrate the advantages of the developed theory.

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Yuga Iguchi, Alexandros Beskos. 2024-09-03. Parameter Inference for Hypo-Elliptic Diffusions under a Weak Design Condition. https://arxiv.org/abs/2312.04444

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