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<p>In this paper, we study a stochastic partial differential equation (SPDE) with piecewise constant coefficients, driven by a nonlinear Gaussian space-time white noise. We investigate the asymptotic behavior of the spatial quadratic variation and, as an application, propose an estimator derived from the limiting results.</p>

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Spatial Quadratic Variation for Stochastic Heat Equations Driven by Multiplicative Noise with Piecewise Constant Coefficients

  • 期刊论文

  • 发表日期：

    2025年11月15日

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  • Yongkang Li,
  • Huisheng Shu,
  • Litan Yan

摘要

In this paper, we study a stochastic partial differential equation (SPDE) with piecewise constant coefficients, driven by a nonlinear Gaussian space-time white noise. We investigate the asymptotic behavior of the spatial quadratic variation and, as an application, propose an estimator derived from the limiting results.