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Pure Mathematics 2025

随机热方程的拟似然估计
Quasi-Likelihood Estimation ofStochastic Heat Equation

DOI: 10.12677/pm.2025.154135, PP. 317-329

盖子若, 杨晗璐, 闫理坦

Keywords: 随机热方程，时空白噪声，马列万分析，拟似然，参数估计
Stochastic Heat Equation, Space-Time White Noise, Malliavin Calculus, Quasi-Likelihood,Parameter Estimates

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Abstract:

我们使用拟似然方法研究了随机热方程的参数估计问题，该方程为： $\frac{？}{？ t} u (t, x) = \frac{1}{2} Δ u (t, x) + \sqrt{θ} \dot{W} (t, x) (t \geq 0, ？ x \in R)$ 其初始条件u(0, x) = 0， ˙W 是时空白噪声，Δ 为拉普拉斯算子。假设解关于时间可以离散观测，我们给出了参数θ 的估计量，并基于Malliavin 微积分得到估计量的渐近行为。
In this paper, we investigate the parameter estimation of stochastic heat equation by using the quasi-likelihood method. The equation is given by: $\frac{？}{？ t} u (t, x) = \frac{1}{2} Δ u (t, x) + \sqrt{θ} \dot{W} (t, x) (t \geq 0, ？ x \in R)$ with u(0, x) = 0, where ˙W is a space-time white noise and Δ is Lapalacian. Assuming that the temporal process can be discretely observed, we provide an estimator for the parameter θ and derive the asymptotic behavior of the estimator based on Malliavin calculus.

References

[1]	Chong, C. (2020) High-Frequency Analysis of Parabolic Stochastic PDEs. The Annals of Statistics,48, 1143-1167. https://doi.org/10.1214/19-aos1841
[2]	Cialenco, I. (2018) Statistical Inference for SPDEs: An Overview. Statistical Inference for Stochastic Processes, 21, 309-329. https://doi.org/10.1007/s11203-018-9177-9
[3]	Cialenco, I. and Glatt-Holtz, N. (2011) Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations. Stochastic Processes and their Applications, 121, 701-724. https://doi.org/10.1016/j.spa.2010.12.007
[4]	Cialenco, I. and Huang, Y. (2019) A Note on Parameter Estimation for Discretely Sampled SPDEs. Stochastics and Dynamics, 20, 2050016. https://doi.org/10.1142/s0219493720500161
[5]	Cialenco, I., Kim, H. and Lototsky, S.V. (2019) Statistical Analysis of Some Evolution Equations Driven by Space-Only Noise. Statistical Inference for Stochastic Processes, 23, 83-103. https://doi.org/10.1007/s11203-019-09205-0
[6]	Cialenco, I., Lototsky, S.V. and Pospí？il, J. (2009) Asymptotic Properties of the Maximum Likelihood Estimator For Stochastic Parabolic Equations with Additive Fractional Brownian Motion. Stochastics and Dynamics, 9, 169-185. https://doi.org/10.1142/s0219493709002610
[7]	Hildebrandt, F. and Trabs, M. (2021) Parameter Estimation for SPDEs Based on Discrete Observations in Time and Space. Electronic Journal of Statistics, 15, 2716-2776. https://doi.org/10.1214/21-ejs1848
[8]	Markussen, B. (2003) Likelihood Inference for a Discretely Observed Stable Processde. Bernoulli, 9, 745-762. https://doi.org/10.3150/bj/1066418876
[9]	Maslowski, B. and Pospí？il, J. (2007) Ergodicity and Parameter Estimates for Infinite- Dimensional Fractional Ornstein-Uhlenbeck Process. Applied Mathematics and Optimization,
[10]	Pospí？il, 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. https://doi.org/10.1080/07362990701282849
[11]	Torres, S., Tudor, C. and Viens, F. (2014) Quadratic Variations for the Fractional-Colored Stochastic Heat Equation. Electronic Journal of Probability, 19, 1-51. https://doi.org/10.1214/ejp.v19-2698
[12]	Nourdin, I. and Peccati, G. (2012) Normal Approximations with Malliavin Calculus. Cambridge University Press. https://doi.org/10.1017/cbo9781139084659

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随机热方程的拟似然估计Quasi-Likelihood Estimation ofStochastic Heat Equation

随机热方程的拟似然估计
Quasi-Likelihood Estimation ofStochastic Heat Equation