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.

几十年来，克利福德分析一直是活跃的研究领域，导致了解决纯数学和应用数学问题的各种方法。然而，随机分析领域尚未在 Clifford 环境中得到全面解决，因为到目前为止只提出了一些贡献。考虑到随机分析工具在对象研究中发挥着重要作用，例如正定函数、再现核和偏微分方程，因此在 Clifford 分析的背景下开发用于研究这些对象的工具非常重要。因此，在这篇正在进行的论文中，我们通过研究 Clifford 设置中的随机变量、鞅、Brownian 运动和 Itô 公式，提出了随机 Clifford 分析的进一步步骤，