Weak approximations and extrapolations of stochastic differential equations with jumps

Numerical discretization schemes are developed to approximate functionals o f stochastic differential equations with jumps, and the convergence is show n to have an appropriate order. For the Euler scheme and the second order w eak scheme, the leading coefficient of their global errors are determined b y the stochastic Taylor expansion. Based on the error expression, the extra polation technique can be applied to get a higher order convergence. Numeri cal examples are provided to compare various weak schemes and extrapolation s.