2021/08/25 by Nishant Agrawal, Agrawal, Nishant, Yaozhong Hu +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2108.11020
openalex publication_date 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we extend the logarithmic Euler-Maruyama scheme for stochastic delay differential equation in one dimension to the part where we propose a scheme for a system of stochastic delay differential equations. We then show that the scheme always maintains positivity subject to initial conditions. We then show the convergence of the proposed Euler-Maruyama scheme. With this scheme, all the approximate solutions are positive and the rate of convergence of this scheme is 0.5.