×

Convergence and stability of implicit methods for jump-diffusion systems. (English) Zbl 1109.65007

The authors consider the strong convergence of implicit methods for the solution of stochastic differential equations with Poissonian jumps. It is demonstrated that implicitness offers benefits for the numerical stability. A mean-square linear stability analysis is undertaken.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
PDFBibTeX XMLCite