Given a stochastic representation for [20]: (28).
The claimed stochastic representation of u is immediate.
A generalized Polynomial Chaos stochastic representation is used as the surrogate model.
Based upon the stochastic representation theorem [5], any x m ~ CE N (γ, Σ, g) with rank = k ≤ N admits the stochastic representation x m = d γ + R Pu, where the non-negative random variable (r.v).
In other cases, the stochastic representation is taken in (Nolan 2016) to motivate an approximative simulation method.
Our goal is to derive a stochastic representation for this problem, similar to the Feynman-Kac formula.
This transformation then provides a stochastic representation (SR) for the random vector uniformly distributed on the tetragon.
The microscopic stochastic representation of stress and strain fields reflects the heterogeneity inherently present in engineering materials at small scales.
Based upon a stochastic representation, the method is extended to the general class of polyhedral convex contoured distributions of known dimension.
Based on the stochastic representation of the monthly river velocity and material strength, a limit-state function is established with the classical blade element momentum method.
