It is convenient to define H(X) = Hα(X) = −∞ when X is discrete, e.g., degenerate. (Our notation differs from that of Karlin and Rinott 1981 here.) We study the entropy of a weighted sum, S = ∑n i=1 aiXi, of i.i.d. random variables Xi, assuming that the density f of Xi is log-concave, i.e., supp(f) = {x : f(x) > 0} is an interval and log f is a concave function on supp(f). The main result is th...

Stability and performance of a system can be inferred from the evolution of statistical characteristic (i.e. mean, variance...) of system states. The polynomial chaos of Wiener provides a computationally effective framework for uncertainty quantification of stochastic dynamics in terms of statistical characteristic. In this work, polynomial chaos is used for uncertainty quantification of fracti...

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 stocha...

Predictive modeling of multiscale and multiphysics systems requires accurate data-driven characterization of the input uncertainties and understanding how they propagate across scales and alter the final solution. We will address three major current limitations in modeling stochastic systems: (1) Most of current uncertainty quantification methods cannot detect and handle discontinuity in the pa...