ABSTRACT

Using a conditional probability structure we build transition probabilities that drive appealing classes of reversible Markov processes. The mechanism used in such a construction allows to find a dual Markov process. This kind of duality is then used to compute the predictor operator of one process via its dual. In particular, we identify the dual of some non-conjugate models, namely the $M/M/\mathrm{\infty }$ queue model and a simple birth, death and immigration process. Such duals ensure that the computation of the predictor operators can be done via finite sums.

中文翻译：

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一类连续时间可逆马尔可夫模型的对偶

摘要

使用条件概率结构，我们建立了转移概率，该转移概率可驱动有吸引力的可逆马尔可夫过程类。在这种构造中使用的机制允许找到双重马尔可夫过程。然后，使用这种对偶性通过其对偶来计算一个过程的预测算子。特别是，我们确定了一些非共轭模型的对偶，即$\mathrm{中号}/\mathrm{中号}/\mathrm{\infty }$排队模型和简单的出生，死亡和移民过程。这样的对偶确保可以通过有限的和来完成预测变量的计算。