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Asymptotic non-equivalence of a diffusion and its Euler scheme experiments with unknown variance

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  • Pillai, Natesh S.
  • Smith, Aaron

Abstract

We show the asymptotic non-equivalence of a simple diffusion and its Euler scheme experiment when the variance is not known. This negative result contrasts sharply with the case of a known diffusion coefficient, where Genon-Catalot and Laredo (2014) established asymptotic equivalence between discrete and continuous experiments. Informally, this means that observing only the Euler discretization entails losing information compared to the fully-observed process in this case. In supplementary material, we extend the comparison to some nonparametric classes of diffusions.

Suggested Citation

  • Pillai, Natesh S. & Smith, Aaron, 2026. "Asymptotic non-equivalence of a diffusion and its Euler scheme experiments with unknown variance," Statistics & Probability Letters, Elsevier, vol. 236(C).
    • Handle: RePEc:eee:stapro:v:236:y:2026:i:c:s0167715226001215
    DOI: 10.1016/j.spl.2026.110757
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