基于拟似然方法的随机热方程参数估计
Parameter Estimation for the Stochastic Heat Equation Based on the Quasi-LikelihoodMethod
摘要: 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。
Abstract: 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.
文章引用：盖子若, 杨晗璐, 闫理坦. 基于拟似然方法的随机热方程参数估计[J]. 应用数学进展, 2025, 14(4): 286-300. https://doi.org/10.12677/AAM.2025.144162

参考文献

[1] Cialenco, I. and Glatt-Holtz, N. (2011) Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations. Stochastic Processes and their Applications, 121, 701-724. [Google Scholar] [CrossRef] 
[2] Cialenco, I. and Huang, Y. (2019) A Note on Parameter Estimation for Discretely Sampled SPDEs. Stochastics and Dynamics, 20, Article 2050016. [Google Scholar] [CrossRef] 
[3] Torres, S., Tudor, C. and Viens, F. (2014) Quadratic Variations for the Fractional-Colored Stochastic Heat Equation. Electronic Journal of Probability, 19, 1-51. [Google Scholar] [CrossRef] 
[4] Gamain, J. and Tudor, C.A. (2023) Exact Variation and Drift Parameter Estimation for the Nonlinear Fractional Stochastic Heat Equation. Japanese Journal of Statistics and Data Sci- ence, 6, 381-406. [Google Scholar] [CrossRef] 
[5] Hu, Y. and Nualart, D. (2010) Parameter Estimation for Fractional Ornstein-Uhlenbeck Pro- cesses. Statistics Probability Letters, 80, 1030-1038. [Google Scholar] [CrossRef] 
[6] Cialenco, I., Lototsky, S.V. and Pospíšil, J. (2009) Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion. Stochastics and Dynamics, 9, 169-185. [Google Scholar] [CrossRef] 
[7] Markussen, B. (2003) Likelihood Inference for a Discretely Observed Stable Processde.
[8] Bernoulli, 9, 745-762.[CrossRef] 
[9] Alòs, E., Mazet, O. and Nualart, D. (2001) Stochastic Calculus with Respect to Gaussian Processes. The Annals of Probability, 29, 766-801. [Google Scholar] [CrossRef] 
[10] Nualart, D. (1995) The Malliavin Calculus and Related Topics. Springer.
[11] Pospíšil, J. and Tribe, R. (2007) Parameter Estimates and Exact Variations for Stochastic Heat Equations Driven by Space-Time White Noise. Stochastic Analysis and Applications, 25, 593-611. [Google Scholar] [CrossRef] 
[12] Nourdin, I. and Peccati, G. (2012) Normal Approximations with Malliavin Calculus. From Stein’s Method to Universality. Cambridge University Press. [Google Scholar] [CrossRef] 

为你推荐