α -scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity

This paper develops an α-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed Lévy noise (TCSDEwLNs). The analysis accommodates time–space-dependent coefficients satisfying local Lipschitz conditions. Properties of the inverse subordinator E are investigated and explicit moment bounds for the exact solution are derived with jump rate incorporated. The analysis demonstrates that the ST method converges strongly with order of min{ηF,ηG,ηH,α/2}, establishing a precise relationship between numerical accuracy and the time-change mechanism. This theoretical advancement extends existing results and facilitates applications in finance, physics and biology where time-changed Lévy models are prevalent.