对称矩阵上扩散问题的Picard迭代
Picard iterations for diffusions on symmetric matrices
摘要：
矩阵值随机过程在物理学、工程学和数理金融等领域有着重要的意义。研究的第一个模型之一是所谓的Wishart过程，它被描述为矩阵空间中随机微分方程的解。本文分析了该模型的自然扩张，证明了其解的存在唯一性。我们通过在对称矩阵空间中进行Picard迭代技术来实现这一点。这种方法考虑了矩阵的算子特征，这有助于证实Lipchitz条件如何在这种情况下自然出现。
英文摘要：
Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the solution of a stochastic differential equation in the space of matrices. In this paper we analyze natural extensions of this model, and prove the existence and uniqueness of the solution. We do this by carrying out a Picard iteration technique in the space of symmetric matrices. This approach takes into account the operator character of the matrices, which helps to corroborate how the Lipchitz conditions also arise naturally in this context.
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