H.T. Banks, Shuhua Hu
Center for Research in Scientific Computation
Center for Quantitative Sciences in Biomedicine
North Carolina State University
Raleigh, NC 27695-8212, USA

Abstract. 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.

Received: September 7, 2012

AMS Subject Classification: stochastic differential equations, random differential equations, probability density functions, Fokker-Planck equation, Liouville equation, structured population model, growth rate distributed structured population model, Markov operators and semigroups, pointwise equivalence

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