Exponential Euler-Maruyama method for stochastic delay Kolmogorov equations with superlinear coefficients

Numerical studies on stochastic differential delay equations (SDDEs) have been widely considered in recent years. However, the results are not applicable to an important class known as stochastic delay Kolmogorov equations since their unique solutions are positive. To fill the gap, in this paper, we aim to construct a positivity preserving numerical method for the stochastic delay Kolmogorov equations under certain restrictions. We will reconstruct the exponential Euler-Maruyama (EM) scheme originally developed by Cai, Mao, & Fei (2023) to study its strong convergence. The main results are finally illustrated by computer simulations.