The correlated random process is represented as a solution of a stochastic differential first-order equation (SDE). The case of processes with probability a density function defined on a semi-infinite or finite range is considered. The limitation of the range of the simulated process requires modification of the specific structure of the SDE. The approach presented provides excellent results in modeling significant non-Gaussian processes with approximately an exponential correlation function. It is validated by direct numerical simulation of a uniformly distributed correlated process.