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Existence and non-existence of the CLT for a family of SDEs driven by stable processes

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  • Mo, Yingjun
  • Wang, Yu

Abstract

We study a family of stochastic differential equations in Rd with non-globally Lipschitz drift driven by rotationally symmetric α-stable noise (α∈(1,2)). The drift satisfies a dissipativity condition ensuring the existence of a unique invariant measure. We establish a central limit theorem for time averages of test functions: it holds for all bounded functions, and for Lipschitz functions it may fail if the dissipativity is weak but holds under stronger dissipativity. The proof combines Stein’s method with martingale CLT.

Suggested Citation

  • Mo, Yingjun & Wang, Yu, 2026. "Existence and non-existence of the CLT for a family of SDEs driven by stable processes," Statistics & Probability Letters, Elsevier, vol. 235(C).
    • Handle: RePEc:eee:stapro:v:235:y:2026:i:c:s0167715226000891
    DOI: 10.1016/j.spl.2026.110725
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