MEAN-SQUARE APPROXIMATIONS OF LEVY NOISE DRIVEN SDES WITH SUPER-LINEARLY GROWING DIFFUSION AND JUMP COEFFICIENTS

This paper first establishes a fundamental mean-square convergence theorem for general one-step numerical approximations of Levy noise driven stochastic differential equations with non-globally Lipschitz coefficients. Then two novel explicit schemes are designed and their convergence rates are exactly identified via the fundamental theorem. Different from existing works, we do not impose a globally Lipschitz condition on the jump coefficient but formulate appropriate assumptions to allow for its super-linear growth. However, we require that the Levy measure is finite. New arguments are developed to handle essential difficulties in the convergence analysis, caused by the super-linear growth of the jump coefficient and the fact that higher moment bounds of the Poisson increments integral(t+h)(t) integral(Z)(N) over bar (ds,dz), t >= 0, h > 0 contribute to magnitude not more than O(h). Numerical results are finally reported to confirm the theoretical findings.