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：我们研究了分支马尔可夫链转移密度的核估计方法。在一些遍历和正则性质下，我们证明了这种估计器是一致的和渐近正常的。接下来，在数值研究中，我们提出了两种数据驱动方法来选择带宽参数。这些方法基于所谓的双带宽方法。