随机迭代模型是由迭代公式定义的随机过程，随着计算机科学和自动化控制理论的发展，凭借着便于构造和模拟的优势，随机迭代模型在许多领域都有着广泛的应用和研究。近三十年来，有关随机迭代模型的统计推断问题已受到越来越多的概率统计学家的关注。本项目计划针对Robbins-Monro (RM)型随机迭代过程和分岔(Bifurcating)自回归过程这两类重要的随机迭代模型的统计问题开展研究。具体内容包括：(1) 研究RM型随机迭代过程（非）参数估计的大样本性质和偏差不等式；(2) 研究随机系数分岔自回归过程和分岔整数值自回归过程（非）参数估计的大样本性质，尤其是大偏差原理和偏差不等式。

Random iterative models are those stochastic processes defined by an iterative formula, which are easy to conceive and simulate. With the development of computer science and automatic control theory, random iteration models have been widely used and studied in many fields. Over the past three decades, the statistical inference problems of random iterative models have attracted more and more attention. The project plans to study statistical problems for the Robbins-Monro (RM) type stochastic approximation and random bifurcating autoregressive processes: (1) researching the large sample theory and deviation inequalities of (non-)parametric estimation for RM type stochastic approximation; (2) researching the large sample theory, especially large deviation principles and deviations inequalities, of (non-)parametric estimation for random coefficient bifurcating autoregressive processes and bifurcating integer-valued autoregressive processes.