Scholarlink

<p>We study a generalized stochastic heat equation driven by space-time white noise and involving a spatially heterogeneous operator. The model describes heat conduction in a medium composed of two different materials. We focus on the temporal power variations of the solution and analyze two types of power variations: the quartic variation and a weighted quadratic variation. For both, we establish Central Limit Theorem and we derive convergence rates under the Wasserstein distance. These theoretical results are then applied to statistical inference for a parametric version of the model with unknown drift parameter. Based on power variations, we construct consistent estimators and study their asymptotic distributions. Our work combines probabilistic analysis with statistical methodology in the context of SPDEs with spatial heterogeneity.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Semilinear stochastic heat equation with piecewise constant coefficients: Power variations and parameter estimation

  • 期刊论文

  • 发表日期：

    2026年3月23日

查看全文
  • Ciprian Tudor,
  • Eya Zougar

摘要

We study a generalized stochastic heat equation driven by space-time white noise and involving a spatially heterogeneous operator. The model describes heat conduction in a medium composed of two different materials. We focus on the temporal power variations of the solution and analyze two types of power variations: the quartic variation and a weighted quadratic variation. For both, we establish Central Limit Theorem and we derive convergence rates under the Wasserstein distance. These theoretical results are then applied to statistical inference for a parametric version of the model with unknown drift parameter. Based on power variations, we construct consistent estimators and study their asymptotic distributions. Our work combines probabilistic analysis with statistical methodology in the context of SPDEs with spatial heterogeneity.