In this paper, we introduce an extension of a Brownian bridge with a random length by including uncertainty also in the pinning level of the bridge. The main result of this work is that unlike for deterministic pinning point, the bridge process fails to be Markovian if the pining point distribution is absolutely continuous with respect to the Lebesgue measure. Further results include the derivation of formulae to calculate the conditional expectation of various functions of the random pinning time, the random pinning location, and the future value of the Brownian bridge, given an observation of the underlying process. For the specific case that the pining point has a two-point distribution, we state further properties of the Brownian bridge, e.g. the right continuity of its natural filtration and its semi-martingale decomposition. The newly introduced process can be used to model the flow of information about the behaviour of a gas storage contract holder; concerning whether to inject or withdraw gas at some random future time.

在本文中，我们通过在桥的钉扎级别中也包含不确定性来介绍具有随机长度的布朗桥的扩展。这项工作的主要结果是，与确定性钉扎点不同，如果钉扎点分布相对于勒贝格测度绝对连续，则桥接过程不能是马尔可夫的。进一步的结果包括推导公式来计算随机钉扎时间、随机钉扎位置和布朗桥的未来值的各种函数的条件期望，并观察基础过程。对于钉扎点具有两点分布的特定情况，我们陈述了布朗桥的进一步性质，例如其自然过滤的正确连续性及其半鞅分解。新引入的流程可用于模拟有关储气合同持有人行为的信息流；关于是否在未来某个随机时间注入或抽出气体。