%0 Journal Article
%T 随机热方程的拟似然估计<br>Quasi-Likelihood Estimation ofStochastic Heat Equation
%A 盖子若
%A 杨晗璐
%A 闫理坦
%J Pure Mathematics
%P 317-329
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.154135
%X 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：<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mfrac><mi mathvariant=\"normal\">？</mi><mrow><mi mathvariant=\"normal\">？</mi><mi>t</mi></mrow></mfrac><mi>u</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant=\"normal\">Δ</mi><mi>u</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>+</mo><msqrt><mi>θ</mi></msqrt><mrow><mover><mi>W</mi><mo>˙</mo></mover></mrow><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"></mspace></mstyle><mo stretchy=\"false\">(</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mtext>&nbsp;</mtext><mi>x</mi><mo>∈</mo><mrow><mi mathvariant=\"double-struck\">R</mi></mrow><mo stretchy=\"false\">)</mo></math>
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。<br>In this paper, we investigate the parameter estimation of stochastic heat equation by
using the quasi-likelihood method. The equation is given by:
<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mfrac><mi mathvariant=\"normal\">？</mi><mrow><mi mathvariant=\"normal\">？</mi><mi>t</mi></mrow></mfrac><mi>u</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant=\"normal\">Δ</mi><mi>u</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>+</mo><msqrt><mi>θ</mi></msqrt><mrow><mover><mi>W</mi><mo>˙</mo></mover></mrow><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mstyle scriptlevel=\"0\"><mspace width=\"1em\"></mspace></mstyle><mo stretchy=\"false\">(</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mtext>&nbsp;</mtext><mi>x</mi><mo>∈</mo><mrow><mi mathvariant=\"double-struck\">R</mi></mrow><mo stretchy=\"false\">)</mo></math>
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.
%K 随机热方程，时空白噪声，马列万分析，拟似然，参数估计<br>Stochastic Heat Equation
%K Space-Time White Noise
%K Malliavin Calculus
%K Quasi-Likelihood
%K Parameter Estimates
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=113229