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This work presents the concept of kernel mean embedding and kernelprobabilistic programming in the context of stochastic systems. We proposeformulations to represent, compare, and propagate uncertainties for fairlygeneral stochastic dynamics in a distribution-free manner. The new tools enjoysound theory rooted in functional analysis and wide applicability asdemonstrated in distinct numerical examples. The implication of this newconcept is a new mode of thinking about the statistical nature of uncertaintyin dynamical systems.

A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming