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arXiv · 2607.00330

Ergodicity and High-Frequency Inference for Hybrid Switching L\'{e}vy-Driven Stochastic Differential Equations

Yuzhong Cheng
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Abstract

Hybrid switching L\'evy-driven stochastic differential equations with pure-jump noise and state-dependent switching rates are studied under high-frequency observation. A three-stage inference procedure is proposed for the drift, scale, and switching-rate parameters, combining a staged Gaussian quasi-likelihood with an intensity-type contrast. Checkable sufficient conditions for weighted exponential ergodicity are established for the hybrid process; the proof does not rely on Brownian smoothing, but uses a fixed skeleton-chain argument combining small-jump accessibility and regime connectivity. Under ergodicity and the high-frequency sampling scheme, consistency, joint asymptotic normality, and a polynomial-type large deviation inequality are proved for the full estimator. The joint limit exhibits a transparent covariance structure: the drift and scale blocks are coupled through the third moment of the driving L\'evy noise, whereas the switching-rate block is asymptotically uncorrelated with the continuous-coefficient blocks. Numerical experiments for models driven by normal inverse Gaussian noise illustrate the finite-sample behavior of the proposed estimators.

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Yuzhong Cheng. 2026-07-01. Ergodicity and High-Frequency Inference for Hybrid Switching L\'{e}vy-Driven Stochastic Differential Equations. https://arxiv.org/abs/2607.00330

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