Domain theory has a long history of applications in theoretical computer science and mathematics. In this article, we explore the relation of domain theory to probability theory and stochastic processes. The goal is to establish a theory in which Polish spaces are replaced by domains, and measurable maps are replaced by Scott-continuous functions. We illustrate the approach by recasting one of the fundamental results of stochastic process theory – Skorohod's Representation Theorem – in domain-theoretic terms. We anticipate the domain-theoretic version of results like Skorohod's Theorem will improve our understanding of probabilistic choice in computational models, and help devise models of probabilistic programming, with its focus on programming languages that support sampling from distributions where the results are applied to Bayesian reasoning.

领域理论在理论计算机科学和数学中的应用历史悠久。在本文中，我们探讨了领域理论与概率论和随机过程的关系。目标是建立一种理论，在该理论中，波兰空间被域替换，可测图被斯科特连续函数替换。我们通过用域理论的术语重铸随机过程理论的基本结果之一-斯科罗霍德的表示定理，来说明这种方法。我们期望结果的领域理论版本（例如Skorohod定理）将增进我们对计算模型中概率选择的理解，并有助于设计概率编程模型，