On one-dimensional random fields with fixed end values

For a one-dimensional, uni-variate random field with deterministic fixed end values, expressions are derived for the conditional mean, variance, and covariance functions in terms of given mean, variance, and correlation functions for an unrestricted, variance-homogeneous Gaussian random field. Also, a relation is derived between the conditional random field and the underlying unrestricted random field. This relation is useful for simulation purposes. Further, expressions are derived for the coefficients in a series expansion for the conditional random field. The present results are obtained from known general formulas for conditional Gaussian distributions, conditional estimation, and series expansion. An earlier alternate approach to enforcing end conditions is also examined. An example is given to illustrate the effect of conditioning a random field by zero end constraints. The present results have direct application to the representation of random imperfections in probabilistic stability analysis of columns and arches.