Online Statistical Inference for Nonlinear Stochastic Approximation with Markovian Data
马尔可夫数据下非线性随机逼近的在线统计推断
Many stochastic approximation (SA) algorithms evolve along a single trajectory, making uncertainty quantification challenging under nonlinear dynamics and Markov dependence. We develop an online inference framework for nonlinear SA with decreasing step sizes. Under local stability and verifiable conditions, we establish a functional central limit theorem for the partial-sum path. The proof uses a Poisson-equation decomposition to handle Markov dependence and a uniform bound…