Compensated projected Euler method for stochastic differential equations with jumps under global monotonicity condition
This work provides a numerical method for a broader class of SDEs with jumps, but the improvement is incremental over existing projected Euler methods.
The paper proposes a compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition that allows superlinear growth of the jump-diffusion coefficient, and proves strong convergence of order 1/2.
This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the jump-diffusion coefficient to be growth superlinearly. Moreover, the method is proved to be convergent with strongly order $\frac{1}{2}$ on the discrete time level. Finally, some numerical experiments are carried out to confirm the theoretical results.