论文标题
确定终端值的随机抛物线方程的溶液
Determination the Solution of a Stochastic Parabolic Equation by the Terminal Value
论文作者
论文摘要
本文通过最终时间的价值$ t $研究了确定随机扩散过程的历史的反面问题。通过建立新的卡尔曼估计，该问题的有条件稳定性得到了证明。基于Tikhonov方法的思想，提出了正则化解决方案。存在对正则化解决方案的存在和唯一性的分析，以及在A-Proior假设下进行错误估计的证明。还说明了正则化的数值验证，包括数值算法和示例。
This paper studies the inverse problem of determination the history for a stochastic diffusion process, by means of the value at the final time $T$. By establishing a new Carleman estimate, the conditional stability of the problem is proven. Based on the idea of Tikhonov method, a regularized solution is proposed. The analysis of the existence and uniqueness of the regularized solution, and proof for error estimate under an a-proior assumption are present. Numerical verification of the regularization, including numerical algorithm and examples are also illustrated.
