Compensated stochastic theta methods for stochastic differential equations with jumps (Q987597)

Compensated stochastic theta methods (CSTM) for approximating the solutions of jumpdiffusion Ito stochastic differential equations of the form \[ dX(t)= f(X(t-))\,dt+ g(X(t-))\,dW(t)+ h(X(t-))\,dN(t),\;t> 0,\;X(0-)= X_0 \] are introduced. Mean-square convergence, A-stability, and exponential stability of CSTM methods are proved. Results of numerical experiments are presented that demonstrate a stability advantage of CSTM over stochastic theta methods.