论文标题
布朗运动，马利亚群岛和伊斯公式在克利福德分析中
Brownian motion, martingales and Itô formula in Clifford analysis
论文作者
论文摘要
几十年来，Clifford分析一直是积极研究的领域，导致各种方法来解决纯数学和应用数学问题。但是，在克利福德环境中，随机分析领域尚未得到解决，因为到目前为止仅提供了少量贡献。考虑到随机分析的工具在对象的研究中起着重要作用，例如积极的确定功能，再现核和部分微分方程，因此在Clifford分析的背景下，开发研究这些对象的工具很重要。因此，在这篇进行中的工作论文中，我们通过研究Clifford环境中的随机变量，Martingales，Brownian Motion和Itôula以及在Clifford分析中的应用，提出了进一步的随机Clifford分析。
Clifford analysis has been the field of active research for several decades resulting in various methods to solve problems in pure and applied mathematics. However, the area of stochastic analysis has not been addressed in its full generality in the Clifford setting, since only a few contributions have been presented so far. Considering that the tools of stochastic analysis play an important role in the study of objects, such as positive definite functions, reproducing kernels and partial differential equations, it is important to develop tools for the study of these objects in the context of Clifford analysis. Therefore, in this work-in-progress paper, we present further steps towards stochastic Clifford analysis by studying random variables, martingales, Brownian motion, and Itô formula in the Clifford setting, as well as their applications in Clifford analysis.
