Lyapunov Conditions for Differentiability of Markov Chain Expectations
研究参数影响下马尔可夫链性能度量的光滑性，给出保证平稳和随机水平折现性能度量可微的条件，并给出导数的概率表示，对数值优化和不确定性量化有用。
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].