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Ergodicity of the stochastic Landau–Lifshitz–Bloch equation with multiplicative and additive noise

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  • Hong, Mingli
  • Qiu, Zhaoyang

Abstract

We study the ergodicity in H1(D) of stochastic Landau–Lifshitz–Bloch equation evolving in either smooth bounded domains or unbounded domains, perturbed by both linear multiplicative and additive noises. Such noise is consistent with the fluctuation–dissipation theorem, which can be used to deduce a Boltzmann distribution valid for the full range of temperatures. We find that an exponential moment could be established in regularity space even for the multiplicative noise case. Then, based on it, we prove the exponential ergodicity.

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  • Hong, Mingli & Qiu, Zhaoyang, 2025. "Ergodicity of the stochastic Landau–Lifshitz–Bloch equation with multiplicative and additive noise," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001476
    DOI: 10.1016/j.spl.2025.110502
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