Efficiently realized approximate models of random functions in stochastic problems of the theory of particle transfer

The paper presents efficiently realized approximations of random functions, which are developed by the authors and numerically modeled for the study of stochastic processes of particle transport, including criticality fluctuations of processes in random media with multiplication. Efficient correlation randomized algorithms for approximating an ensemble of particle trajectories using the correlation function or only the correlation scale of a medium are constructed. A simple grid model of an isotropic random field is formulated reproducing a given average correlation length, which ensures high accuracy in solving stochastic transfer problems for a small correlation scale. The algorithms are tested by solving a test problem of photon transfer and a problem of estimating the overexponential average particle flux in a random medium with multiplication.