由随机测度驱动的热方程的渐近性质
Asymptotic properties of the heat equation driven by stochastic measure
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中文总结 AI 辅助
研究[-L,L]上由随机测度驱动的热方程，通过证明当L趋于无穷时解的趋向性及给出收敛速率估计，在仅假设随机测度概率上σ-可加性的条件下得出相关结论。
中文摘要 AI 辅助
对于在[-L,L]上具有狄利克雷边界条件且由随机测度驱动的热方程，我们证明当L趋于无穷时，其解趋向于在实数域上定义的热方程的解，并得到收敛速率的估计。对于随机测度，我们仅假设概率上的σ-可加性。
英文摘要
For the heat equations driven by a stochastic measure on $[-L, L]$ with the Dirichlet boundary condition, we prove that solutions tend to the solution of the heat equations defined on ${\mathbb R}$ as $L\to \infty$. The estimate of the convergence rate is obtained. For a stochastic measure, we assume the $σ$-additivity in probability only.
