AI 中文总结
针对由时间分数线性随机微分方程描述的线性滤波问题，推导了相关积分方程，并将时间分数状态估计框架应用于建模发展性计算障碍儿童的学习轨迹。
AI 中文摘要
我们研究一类线性滤波问题，其中信号过程由布朗运动驱动的时间分数线性随机微分方程描述。我们推导了条件均值的随机积分方程，以及均方误差函数的Riccati-Volterra型积分方程。作为核心应用，我们提出一种时间分数状态估计框架，用于建模发展性计算障碍儿童的学习轨迹。
英文摘要
We study a linear filtering problem in which the signal process is described by a time-fractional linear stochastic differential equation driven by Brownian motion. We derive a stochastic integral equation for the conditional mean alongside a Riccati--Volterra type integral equation for the mean-square error function. As a core application, we introduce a time-fractional state-estimation framework for modelling learning trajectories in children with developmental dyscalculia.
