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 have been developed by the authors and are numerically simulated for study of stochastic processes of particle transfer, including the problems of process criticality fluctuations in random media with multiplication. Efficient correlation-randomized algorithms are constructed for approximating an ensemble of particle trajectories using a correlation function or only a correlation scale of medium. A simple grid model of an isotropic random field is formulated, which reproduces a given average correlation length. This 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.