Lyapunov Conditions for Differentiability of Markov Chain Expectations
Lyapunov Conditions for Differentiability of Markov Chain Expectations
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DOI：
10.1287/moor.2022.1328
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发表时间：
2017-07
影响因子：
1.7
通讯作者：
C. Rhee;P. Glynn
中科院分区：
文献类型：
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作者：
C. Rhee;P. Glynn
我们考虑一类马尔可夫链，其转移动力学受模型参数的影响。了解这种马尔可夫链的（复杂的）性能指标的参数依赖性往往是显着的兴趣。业绩指标的导数及其连续性w.r.t.例如，当来自统计估计过程的参数中存在不确定性时，参数在性能测量的数值优化和性能测量中的不确定性的量化中起重要作用。在本文中，我们建立的条件，保证光滑的各种类型的棘手的性能指标，如固定和随机时域折扣性能指标的一般状态空间马尔可夫链，并提供概率表示的衍生物。资金来源：C.- H. Rhee由美国国家科学基金会资助[Grant CMMI-2146530]。
We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The derivatives and their continuity of the performance measures w.r.t. the parameters play important roles, for example, in numerical optimization of the performance measures, and quantification of the uncertainties in the performance measures when there are uncertainties in the parameters from the statistical estimation procedures. In this paper, we establish conditions that guarantee the smoothness of various types of intractable performance measures—such as the stationary and random horizon discounted performance measures—of general state space Markov chains and provide probabilistic representations for the derivatives. Funding: C.-H. Rhee is supported by the National Science Foundation [Grant CMMI-2146530].