- In this paper we address novel results on the theoretical structural analysis of dynamic joint probabilistic constraints under continuous random variables. This dynamic probabilistic function is important when decisions are time-dependent and when the modeler can react on past observations. We first study the continuity of dynamic probabilistic constraints and provide strong and weak semi-continuous results depending on whether the policies are supposed to be in the L^p or W^{1,p} spaces. Moreover, we prove the non-convexity of the feasible set of decisions induced by a dynamic probability function in the L^p space. Lastly, for a simple two-stage model, verifiable conditions for Lipschitz continuity and differentiability of this probability function are derived and endowed with explicit derivative formulae.
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