This work concerns with Markov chains on a finite state space. It is supposed that a state-dependent cost is associated with each transition, and that the evolution of the system is watched by an agent with positive and constant risk-sensitivity. For a general transition matrix, the problem of approximating the risk-sensitive average criterion in terms of the risk-sensitive discounted index is studied. It is proved that, as the discount factor increases to 1, an appropriate normalization of the discounted value functions converges to the average cost, extending recent results derived under the assumption that the state space is communicating.

中文翻译：

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具有有限状态空间的风险敏感平均马尔可夫成本链中的折现近似

这项工作涉及有限状态空间上的马尔可夫链。假定与状态相关的成本与每个过渡相关联，并且系统的演变是由具有积极且持续的风险敏感性的代理商来监视的。对于一般的转换矩阵，研究了根据风险敏感折现指数近似风险敏感平均标准的问题。事实证明，当折现因子增加到1时，折现值函数的适当归一化收敛到平均成本，从而扩展了在状态空间正在通信的假设下得出的最新结果。