On the Strong Approximation of Pure Jump Processes

This paper constructs strong discrete time approximations for pure jump processes that can be described by stochastic differential equations. Strong approximations based on jump-adapted time discretizations, which produce no discretization bias, are analyzed. The computational complexity of these approximations is proportional to the jump intensity. Furthermore, by exploiting a stochastic expansion for pure jump processes, higher order discrete time approximations, whose computational complexity is not dependent on the jump intensity, are proposed. The strong order of convergence of the resulting schemes is analyzed.