Higham, Desmond J.; Kloeden, Peter E. Convergence and stability of implicit methods for jump-diffusion systems. (English) Zbl 1109.65007 Int. J. Numer. Anal. Model. 3, No. 2, 125-140 (2006). 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. Reviewer: Eckhard Platen (Broadway) Cited in 1 ReviewCited in 64 Documents 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) Keywords:jump-diffusions; implicit Euler scheme; strong convergence; numerical stability; stochastic differential equations PDFBibTeX XMLCite \textit{D. J. Higham} and \textit{P. E. Kloeden}, Int. J. Numer. Anal. Model. 3, No. 2, 125--140 (2006; Zbl 1109.65007)