On the numerical generation of positive-axis-defined distributions with an exponential autocorrelation function

Stochastic modeling commonly requires random process generation with an exponential autocorrelation function (ACF). These random processes may be represented as a solution of a stochastic differential equation (SDE) of the first order and usually have one-sided (positive-axis-defined) distributions. However, adoption of the SDE-based method faces serious limitations due to difficulties with the numerical solution. To overcome this issue we propose a tractable general numerical solution of the above-mentioned SDE that preserves solution positivity and accuracy, and validate it with numerical simulations.