不精确概率树：桥接两种不精确概率理论
Imprecise probability trees: Bridging two theories of imprecise probability
摘要：
我们给出了一个概述的两种方法，概率论，在较低和较高的概率，而不是概率，使用：瓦利的行为理论的不精确的概率，谢弗和Vovk的博弈论的概率。我们表明，这两个理论是更密切相关的比会怀疑乍一看，我们建立了它们之间的对应关系，（i）有一个有趣的解释，（ii）允许我们自由进口的结果从一个理论到另一个。我们的方法导致一个帐户的概率树和随机过程中的框架瓦利的理论。我们表明我们的结果可以用来减少处理概率树中的不精确性的计算复杂性，我们证明了一个有趣的和相当普遍的版本的弱大数定律。
英文摘要：
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.
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