标题： 不精确概率树：连接两种不精确概率理论 显示英文标题

标题： Imprecise probability trees: Bridging two theories of imprecise probability

摘要： 我们概述了两种概率理论的方法，其中使用下限和上限概率而不是概率：Walley的不精确概率行为理论，以及Shafer和Vovk的概率博弈论解释。 我们表明这两种理论比表面上看起来更加密切相关，并建立了它们之间的一种对应关系，该对应关系（i）具有有趣的解释，（ii）使我们能够自由地将一个理论中的结果导入另一个理论中。 我们的方法导致了Walley理论框架下的概率树和随机过程的解释。 我们指出如何利用我们的结果来降低处理概率树中不精确性的计算复杂性，并证明了一个有趣且相当普遍的大数定律弱版本。 显示英文摘要

摘要： We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that (i) has an interesting interpretation, and (ii) allows us to freely import results from one theory into the other. Our approach leads to an account of probability trees and random processes in the framework of Walley's theory. We indicate how our results can be used to reduce the computational complexity of dealing with imprecision in probability trees, and we prove an interesting and quite general version of the weak law of large numbers.