Convergence and stability of the partially truncated Euler-Maruyama method for stochastic differential equations with piecewise continuous arguments driven by Poisson jumps

Key Points

• The convergence of the partially truncated Euler-Maruyama method indicates improved numerical solutions for stochastic differential equations.
• Stability results were observed under specific piecewise continuous conditions with regard to Poisson jumps influencing the method's performance.
• Assessment using the Euler-Maruyama method demonstrated effective handling of stochastic behaviors in differential equations influenced by random jumps.
• These findings support the potential application of the method in various fields, emphasizing future computational and theoretical work needed.