Uncertainty Propagation and Quantification in a Continuous Time Dynamical System

Uncertainty propagation and quantification has gained considerable research attention during recent years. In this paper we consider uncertainty propagation and quantification in a continuous-time dynamical system governed by ordinary differential equations with uncertain/stochastic components. Specifically, we focus on the time evolution of probability density functions of the resulting stochastic processes, and discuss their applications in different fields with particular focus on population dynamics. In addition, we compare the difference in the stochastic processes resulting from differential equations with different types of random inputs, and discuss the connections among them.