The class of location-scale finite mixtures is enduring interest both from applied and theoretical perspectives probability statistics. We establish prove the following results: to an arbitrary degree accuracy, (a) a continuous density function (PDF) can approximate any PDF, uniformly, on compact set; (b) for p?1, essentially bounded PDF in Lp, Lp norm.

We propose a stochastic prediction-control framework to promote safety in automated driving by directly controlling the joint state probability density functions (PDFs) subject vehicle dynamics via trajectory-level feedback. To illustrate main ideas, we focus on multi-lane highway scenario although proposed can be adapted other contexts. The computational pipeline consists of PDF prediction lay...