Compensated projected Euler method for stochastic differential equations with jumps under global monotonicity condition

TL;DR

This paper introduces a new Euler-Maruyama method for stochastic differential equations with jumps, allowing superlinear growth in coefficients, and proves its convergence with numerical validation.

Contribution

It proposes a compensated projected Euler-Maruyama method that works under a global monotonicity condition accommodating superlinear growth, with proven convergence and numerical confirmation.

Findings

Method converges with strong order 1/2

Allows superlinear growth in jump-diffusion coefficients

Numerical experiments confirm theoretical convergence

Abstract

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.