General models of random fields on the sphere associated with nonlocal equations in time and space are studied. The properties of the corresponding angular power spectrum are discussed and asymptotic results in terms of random time changes are found.
Sufficient conditions are given for the existence of a unique bounded in the mean solution to a second-order difference equation with jumps of operator coefficients in a Banach space. The question of the proximity of this solution to the stationary solution of the corresponding difference equation with constant operator coefficients is studied.