Parameter Estimation for the Stochastic Heat Equation Based on the Quasi-LikelihoodMethod

本文中，我们研究了时空白噪声驱动的随机热方程的参数估计问题。在固定某一时间点的情况下， 我们假设空间过程可以离散观测，使用拟似然方法给出了扩散参数的估计量。另外，我们基于马 列万分析得到了估计量的渐进行为。In this paper, we investigate the parameter estimation problem of the stochastic heat equation driven by space-time white noise. Under the assumption that the spatial process can be discretely observed at a fixed time point, we use the quasi-likelihood method to provide an estimator for the diffusion parameter. Additionally, we derive the asymptotic behavior of the estimator based on Malliavin calculus.