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Zbl 1109.65007
Higham, Desmond J.; Kloeden, Peter E.
Convergence and stability of implicit methods for jump-diffusion systems. (English)
[J] Int. J. Numer. Anal. Model. 3, No. 2, 125-140 (2006). ISSN 1705-5105

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.
[Eckhard Platen (Broadway)]
MSC 2000:
*65C30 Stochastic differential and integral equations
65L20 Stability of numerical methods for ODE
34F05 ODE with randomness
60H10 Stochastic ordinary differential equations
60H35 Computational methods for stochastic equations

Keywords: jump-diffusions; implicit Euler scheme; strong convergence; numerical stability; stochastic differential equations

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