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On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations
International Scientific Research Publications (2018-06-19)In this paper, the application of adaptive generalized polynomial chaos (gPC) to quantify the uncertainty for non-linear random difference equations is analyzed. It is proved in detail that, under certain assumptions, the ... -
Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties
Springer (2018-10-24)In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference equations. The coefficients are assumed to be stochastic processes, ...