We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we propose two data-driven methods to choose the bandwidth parameters. These methods are based on the so-called two bandwidths approach.

翻译：我们研究分叉马尔可夫链转移密度的核估计量。在遍历性与正则性条件下，我们证明了该估计量具有相合性和渐近正态性。在数值实验中，我们提出了两种基于所谓双带宽方法的数据驱动型带宽参数选择方法。